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Common Core: 8th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #292 : Triangles

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$\sqrt{66}$

$\sqrt{65}$

$\sqrt{69}$

Correct answer:

$\sqrt{65}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{7^2 + 4^2}=\sqrt{65}$

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Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Right_triangle

Refer to the above diagram, which depicts a right triangle. What is the value of ?

Possible Answers:

$10\sqrt{2}$

$3 \sqrt{ 13}$

$9\sqrt{3}$

Correct answer:

$3 \sqrt{ 13}$

Explanation:

By the Pythagorean Theorem, which says a^2+b^2=c^2 . being the hypotenuse, or in this problem.

$x^{2} = 6^{2} + 9^{2}$

$x^{2} = 36 + 81$

$x^{2} = 117$

$x =\sqrt{ 117}$

Simply

$\sqrt{ 9} \cdot \sqrt{ 13}$

$3 \sqrt{ 13}$

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Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$4\sqrt5$

$3\sqrt{21}$

$2\sqrt{29}$

$\sqrt{29}$

Correct answer:

$2\sqrt{29}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{10^2 + 4^2}=\sqrt{116}$

Simply:

$\sqrt{4}\cdot\sqrt{29}$

$2\sqrt{29}$

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Example Question #431 : Grade 8

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$11\textup{ cm}$

$13\textup{ cm}$

$12\textup{ cm}$

$10\textup{ cm}$

$14\textup{ cm}$

Correct answer:

$12\textup{ cm}$

Explanation:

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or $90^\circ$ angle. When a triangle includes a right angle, the triangle is said to be a "right triangle."

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

9^2+8^2=c^2

81+64=c^2

145=c^2

$\sqrt{145}=\sqrt{c^2}$

12.04=c

c=12

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Example Question #21 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$37\textup{ cm}$

$35\textup{ cm}$

$34\textup{ cm}$

$33\textup{ cm}$

$36\textup{ cm}$

Correct answer:

$37\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

12^2+35^2=c^2

$144+1\textup,225=c^2$

$1\textup,369=c^2$

$\sqrt{1\textup,369}=\sqrt{c^2}$

37=c

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Example Question #121 : Geometry

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$17\text{ cm}$

$18\text{ cm}$

$14\text{ cm}$

$15\text{ cm}$

$16\text{ cm}$

Correct answer:

$17\text{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

8^2+15^2=c^2

64+225=c^2

289=c^2

$\sqrt{289}=\sqrt{c^2}$

17=c

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Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$43\textup{ cm}$

$40\textup{ cm}$

$42\textup{ cm}$

$41\textup{ cm}$

$39\textup{ cm}$

Correct answer:

$40\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

24^2+32^2=c^2

$576+1\textup,024=c^2$

$1\textup,600=c^2$

$\sqrt{1\textup,600}=\sqrt{c^2}$

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Example Question #32 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$77\textup{ cm}$

$79\textup{ cm}$

$78\textup{ cm}$

$75\textup{ cm}$

$76\textup{ cm}$

Correct answer:

$75\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

72^2+21^2=c^2

$5\textup,184+441=c^2$

$5\textup,625=c^2$

$\sqrt{5\textup,625}=\sqrt{c^2}$

75=c

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Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$12\textup{ cm}$

$16\textup{ cm}$

$13\textup{ cm}$

$15\textup{ cm}$

$14\textup{ cm}$

Correct answer:

$13\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

12^2+5^2=c^2

144+25=c^2

169=c^2

$\sqrt{169}=\sqrt{c^2}$

13=c

Report an Error

Example Question #33 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Possible Answers:

$19\textup{ cm}$

$18\textup{ cm}$

$17\textup{ cm}$

$21\textup{ cm}$

$20\textup{ cm}$

Correct answer:

$20\textup{ cm}$

Explanation:

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

16^2+12^2=c^2

256+144=c^2

400=c^2

$\sqrt{400}=\sqrt{c^2}$

20=c

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Common Core: 8th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #292 : Triangles

Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #431 : Grade 8

Example Question #21 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #121 : Geometry

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #32 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #31 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #33 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

All Common Core: 8th Grade Math Resources

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