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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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 ?

Possible Answers:

75.11

74.01

78.91

72.01

Correct answer:

75.11

Explanation:

Recall how to find the perimeter of a triangle:

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

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

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.

a^2+b^2=c^2

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

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

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

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=4\sqrt2$

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

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

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Example Question #1122 : Basic Geometry

What is the perimeter of a right isosceles triangle with leg lengths of ?

Possible Answers:

42.42

41.09

44.38

48.21

Correct answer:

44.38

Explanation:

Recall how to find the perimeter of a triangle:

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

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

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.

a^2+b^2=c^2

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

a^2+a^2=2a^2=c^2

Now, solve for since the question asks for the length of the hypotenuse.

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

$c=a\sqrt2$

Now, plug in the given value for to find the length of the hypotenuse.

$c=13\sqrt2$

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

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

Report an Error

Example Question #1121 : Basic Geometry

Find the perimeter.

Possible Answers:

40.97

45.06

29.12

35.99

Correct answer:

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=12\sqrt2$

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

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

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

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

Make sure to round to two places after the decimal.

Report an Error

Example Question #141 : Triangles

Find the perimeter.

Possible Answers:

45.71

48.72

44.38

46.22

Correct answer:

44.38

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=13\sqrt2$

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

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

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

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

Make sure to round to two places after the decimal.

Report an Error

Example Question #1121 : Plane Geometry

Find the perimeter.

Possible Answers:

72.49

71.70

69.82

74.58

Correct answer:

71.70

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=21\sqrt2$

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

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

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

$\text{Perimeter}=21+21+21\sqrt2=71.70$

Make sure to round to two places after the decimal.

Report an Error

Example Question #1122 : Plane Geometry

Find the perimeter.

Possible Answers:

78.21

75.11

88.47

80.45

Correct answer:

75.11

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=22\sqrt2$

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

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

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

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

Make sure to round to two places after the decimal.

Report an Error

Example Question #144 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

81.94

89.56

82.40

77.21

Correct answer:

81.94

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=24\sqrt2$

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

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

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

$\text{Perimeter}=24+24+24\sqrt2=81.94$

Make sure to round to two places after the decimal.

Report an Error

Example Question #142 : Triangles

Find the perimeter.

Possible Answers:

80.59

78.53

71.22

79.29

Correct answer:

78.53

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=23\sqrt2$

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

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

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

$\text{Perimeter}=23+23+23\sqrt2=78.53$

Make sure to round to two places after the decimal.

Report an Error

Example Question #146 : 45/45/90 Right Isosceles Triangles

Find the perimeter.

Possible Answers:

79.84

85.36

84.22

85.30

Correct answer:

85.36

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=25\sqrt2$

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

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

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

$\text{Perimeter}=25+25+25\sqrt2=85.36$

Make sure to round to two places after the decimal.

Report an Error

Example Question #1123 : Plane Geometry

Find the perimeter.

Possible Answers:

88.77

76.66

90.90

94.21

Correct answer:

88.77

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 .

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

a^2+a^2=b^2

b^2=2a^2

$b=a\sqrt2$

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

$b=26\sqrt2$

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

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

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

$\text{Perimeter}=26+26+26\sqrt2=88.77$

Make sure to round to two places after the decimal.

Report an Error

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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

Example Question #1122 : Basic Geometry

Example Question #1121 : Basic Geometry

Example Question #141 : Triangles

Example Question #1121 : Plane Geometry

Example Question #1122 : Plane Geometry

Example Question #144 : 45/45/90 Right Isosceles Triangles

Example Question #142 : Triangles

Example Question #146 : 45/45/90 Right Isosceles Triangles

Example Question #1123 : Plane Geometry

All Basic Geometry Resources

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