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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1111 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 8$?

Possible Answers:

27.31 $\displaystyle 27.31$

28.19 $\displaystyle 28.19$

26.46 $\displaystyle 26.46$

29.02 $\displaystyle 29.02$

Correct answer:

27.31 $\displaystyle 27.31$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=8\sqrt2$ $\displaystyle c=8\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=8+8+8\sqrt2=27.31$ $\displaystyle \text{Perimeter}=8+8+8\sqrt2=27.31$

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Example Question #131 : Triangles

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 9$?

Possible Answers:

29.05 $\displaystyle 29.05$

18.15 $\displaystyle 18.15$

40.99 $\displaystyle 40.99$

30.73 $\displaystyle 30.73$

Correct answer:

30.73 $\displaystyle 30.73$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=9\sqrt2$ $\displaystyle c=9\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=9+9+9\sqrt2=30.73$ $\displaystyle \text{Perimeter}=9+9+9\sqrt2=30.73$

Report an Error

Example Question #1113 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 11$?

Possible Answers:

39.71 $\displaystyle 39.71$

38.87 $\displaystyle 38.87$

37.56 $\displaystyle 37.56$

35.45 $\displaystyle 35.45$

Correct answer:

37.56 $\displaystyle 37.56$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=11\sqrt2$ $\displaystyle c=11\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=11+11+11\sqrt2=37.56$ $\displaystyle \text{Perimeter}=11+11+11\sqrt2=37.56$

Report an Error

Example Question #1112 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 14$?

Possible Answers:

49.02 $\displaystyle 49.02$

47.71 $\displaystyle 47.71$

47.80 $\displaystyle 47.80$

51.92 $\displaystyle 51.92$

Correct answer:

47.80 $\displaystyle 47.80$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=14\sqrt2$ $\displaystyle c=14\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=14+14+14\sqrt2=47.80$ $\displaystyle \text{Perimeter}=14+14+14\sqrt2=47.80$

Report an Error

Example Question #1115 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 20$?

Possible Answers:

60.91 $\displaystyle 60.91$

65.01 $\displaystyle 65.01$

68.28 $\displaystyle 68.28$

99.28 $\displaystyle 99.28$

Correct answer:

68.28 $\displaystyle 68.28$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=20\sqrt2$ $\displaystyle c=20\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=20+20+20\sqrt2=68.28$ $\displaystyle \text{Perimeter}=20+20+20\sqrt2=68.28$

Report an Error

Example Question #1116 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 19$?

Possible Answers:

66.71 $\displaystyle 66.71$

64.87 $\displaystyle 64.87$

68.12 $\displaystyle 68.12$

65.50 $\displaystyle 65.50$

Correct answer:

64.87 $\displaystyle 64.87$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=19\sqrt2$ $\displaystyle c=19\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=19+19+19\sqrt2=64.87$ $\displaystyle \text{Perimeter}=19+19+19\sqrt2=64.87$

Report an Error

Example Question #1117 : Plane Geometry

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 16$?

Possible Answers:

54.63 $\displaystyle 54.63$

56.91 $\displaystyle 56.91$

59.42 $\displaystyle 59.42$

55.87 $\displaystyle 55.87$

Correct answer:

54.63 $\displaystyle 54.63$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=16\sqrt2$ $\displaystyle c=16\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=16+16+16\sqrt2=54.63$ $\displaystyle \text{Perimeter}=16+16+16\sqrt2=54.63$

Report an Error

Example Question #11 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 22$?

Possible Answers:

75.11 $\displaystyle 75.11$

74.01 $\displaystyle 74.01$

78.91 $\displaystyle 78.91$

72.01 $\displaystyle 72.01$

Correct answer:

75.11 $\displaystyle 75.11$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=4\sqrt2$ $\displaystyle c=4\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=22+22+22\sqrt2=75.11$ $\displaystyle \text{Perimeter}=22+22+22\sqrt2=75.11$

Report an Error

Example Question #11 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of $\displaystyle 13$?

Possible Answers:

48.21 $\displaystyle 48.21$

44.38 $\displaystyle 44.38$

41.09 $\displaystyle 41.09$

42.42 $\displaystyle 42.42$

Correct answer:

44.38 $\displaystyle 44.38$

Explanation:

Recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+b+c$ $\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

a=b $\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

$\displaystyle a^2+b^2=c^2$

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$c=\sqrt{2a^2}$ $\displaystyle c=\sqrt{2a^2}$

$c=a\sqrt2$ $\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$c=13\sqrt2$ $\displaystyle c=13\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\text{Perimeter}=13+13+13\sqrt2=44.38$ $\displaystyle \text{Perimeter}=13+13+13\sqrt2=44.38$

Report an Error

Example Question #1121 : Basic Geometry

Find the perimeter.

Possible Answers:

40.97 $\displaystyle 40.97$

45.06 $\displaystyle 45.06$

29.12 $\displaystyle 29.12$

35.99 $\displaystyle 35.99$

Correct answer:

40.97 $\displaystyle 40.97$

Explanation:

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then $\displaystyle 12$.

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

$\displaystyle a^2+a^2=b^2$

$\displaystyle b^2=2a^2$

$b=a\sqrt2$ $\displaystyle b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$b=12\sqrt2$ $\displaystyle b=12\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\text{Perimeter}=a+a+b$ $\displaystyle \text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\text{Perimeter}=12+12+12\sqrt2=40.97$ $\displaystyle \text{Perimeter}=12+12+12\sqrt2=40.97$

Make sure to round to two places after the decimal.

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1111 : Plane Geometry

Example Question #131 : Triangles

Example Question #1113 : Plane Geometry

Example Question #1112 : Plane Geometry

Example Question #1115 : Plane Geometry

Example Question #1116 : Plane Geometry

Example Question #1117 : Plane Geometry

Example Question #11 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #11 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #1121 : Basic Geometry

All Basic Geometry Resources

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