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Basic Geometry : Basic Geometry

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 #1 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

What is the length of the hypotenuse of an isosceles right triangle with an area of $10.125\:in$ ?

Possible Answers:

$4.5\sqrt{2}\:in$

$9\:in$

$9.25\sqrt{2}\:in$

$4.5\sqrt{5}\:in$

$18\sqrt{3}\:in$

Correct answer:

$4.5\sqrt{2}\:in$

Explanation:

Recall that an isosceles right triangle is also a 45-45-90 triangle. It has sides that appear as follows:

_tri51

Therefore, the area of the triangle is:

$A=\frac{1}{2}x^2$ , since the base and the height are the same.

For our data, this means:

$10.125=\frac{1}{2}x^2$

Solving for , you get:

20.25=x^2

x=4.5

So, your triangle looks like this:

_tri31

Now, you can solve this with a ratio and easily find that it is $4\sqrt{2}$ . You also can use the Pythagorean Theorem. To do the latter, it is:

h^2 = 4.5^2+4.5^2

$h = \sqrt{4.5^2+4.5^2}$

Now, just do your math carefully:

$h = \sqrt{4.5^2(1+1)}$

That is a weird kind of factoring, but it makes sense if you distribute back into the group. This means you can simplify:

$h = \sqrt{4.5^2(2)} = \sqrt{4.5^2}\sqrt{2}=4.5\sqrt{2}\:in$

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Example Question #4 : 45/45/90 Right Isosceles Triangles

When the sun shines on a 4ft pole, it leaves a shadow on the ground that is also 4ft . What is the distance from the top of the pole to the end of its shadow?

Possible Answers:

5.66 ft

4 ft

5.22 ft

16 ft

6.14 ft

Correct answer:

5.66 ft

Explanation:

The pole and its shadow make a right angle. Because they are the same length, they form an isosceles right triangle (45/45/90). We can use the Pythagorean Theorem to find the hypotenuse. a^2+b^2=c^2 . In this case, a=b=4 . Therefore, we do 4^2+4^2=c^2=32 . So $c=\sqrt{32}\approx5.66$ .

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Example Question #1 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{10}$

$3\sqrt{3}$

$5\sqrt2$

Correct answer:

$5\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{5^2+5^2}$

$\text{Hypotenuse}=\sqrt{25+25}$

Solve.

$\text{Hypotenuse}=\sqrt{50}$

Simplify.

$\text{Hypotenuse}=5\sqrt2$

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Example Question #991 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt3$

$6\sqrt3$

$6\sqrt2$

Correct answer:

$6\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{6^2+6^2}$

$\text{Hypotenuse}=\sqrt{36+36}$

Solve.

$\text{Hypotenuse}=\sqrt{72}$

Simplify.

$\text{Hypotenuse}=6\sqrt2$

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Example Question #991 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt6$

$2\sqrt6$

$12\sqrt2$

$12\sqrt3$

Correct answer:

$12\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{12^2+12^2}$

$\text{Hypotenuse}=\sqrt{144+144}$

Solve.

$\text{Hypotenuse}{}=\sqrt{288}$

Simplify.

$\text{Hypotenuse}=12\sqrt2$

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Example Question #991 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$\sqrt{26}$

$13\sqrt3$

$13\sqrt2$

Correct answer:

$13\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{13^2+13^2}$

$\text{Hypotenuse}=\sqrt{169+169}$

Solve.

$\text{Hypotenuse}=\sqrt{338}$

Simplify.

$\text{Hypotenuse}=13\sqrt2$

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Example Question #11 : 45/45/90 Right Isosceles Triangles

Find the length of the hypotenuse.

Possible Answers:

$14\sqrt3$

$2\sqrt7$

$7\sqrt7$

$14\sqrt2$

Correct answer:

$14\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{14^2+14^2}$

$\text{Hypotenuse}=\sqrt{196+196}$

Solve.

$\text{Hypotenuse}=\sqrt{392}$

Simplify.

$\text{Hypotenuse}=14\sqrt2$

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Example Question #992 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt3$

$14\sqrt6$

$24\sqrt2$

$4\sqrt{10}$

Correct answer:

$24\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{24^2+24^2}$

$\text{Hypotenuse}=\sqrt{576+576}$

Solve.

$\text{Hypotenuse}=\sqrt{1152}$

Simplify.

$\text{Hypotenuse}=24\sqrt2$

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Example Question #11 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$22\sqrt2$

$2\sqrt{11}$

$15\sqrt2$

$4\sqrt{10}$

Correct answer:

$22\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{22^2+22^2}$

$\text{Hypotenuse}=\sqrt{484+484}$

Solve.

$\text{Hypotenuse}=\sqrt{968}$

Simplify.

$\text{Hypotenuse}=22\sqrt2$

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Example Question #994 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$25\sqrt2$

$5\sqrt2$

Correct answer:

$25\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

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

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{25^2+25^2}$

$\text{Hypotenuse}=\sqrt{625+625}$

Solve.

$\text{Hypotenuse}=\sqrt{1250}$

Simplify.

$\text{Hypotenuse}=25\sqrt2$

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Hypotenuse Of A 45/45/90 Right Isosceles Triangle : Pythagorean Theorem

Example Question #4 : 45/45/90 Right Isosceles Triangles

Example Question #1 : Triangles

Example Question #991 : Basic Geometry

Example Question #991 : Basic Geometry

Example Question #991 : Basic Geometry

Example Question #11 : 45/45/90 Right Isosceles Triangles

Example Question #992 : Basic Geometry

Example Question #11 : Triangles

Example Question #994 : Basic Geometry

All Basic Geometry Resources

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