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Common Core: 8th Grade Math : Apply the Pythagorean Theorem to Determine Unknown Side Lengths in Right Triangles: CCSS.Math.Content.8.G.B.7

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

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #92 : Geometry

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Possible Answers:

0.5

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Possible Answers:

4.64 units

5.38 units

units

5.20 units

Correct answer:

5.38 units

Explanation:

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs with the lengths $4\:cm$ and $5\:cm$ . Find the length of the hypotenuse.

Possible Answers:

$41\:cm$

$\sqrt{35}\:cm$

$\sqrt{41}\:cm$

$3\:cm$

Correct answer:

$\sqrt{41}\:cm$

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}\:cm$

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Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse in the right triangle below.

Possible Answers:

25.61

22.78

23.45

Correct answer:

25.61

Explanation:

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

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

If a right triangle has a base of and a height of , what is the length of the hypotenuse?

Possible Answers:

$\sqrt{11}$

$\sqrt{65}$

$\sqrt{14}$

Correct answer:

$\sqrt{65}$

Explanation:

To solve this problem, we must utilize the Pythagorean Theorom, which states that:

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

We know that the base is , so we can substitute in for . We also know that the height is , so we can substitute in for .

$7^{2}+4^{2}=c^{2}$

Next we evaluate the exponents:

$7^{2}=49$

$4^{2}=16$

Now we add them together:

49+16=65

Then, $65=c^{2}$ .

is not a perfect square, so we simply write the square root as $\sqrt{65}$ .

$c=\sqrt{65}$

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Example Question #101 : Geometry

If a right triangle has a base of and a height of , what is the length of the hypotenuse?

Possible Answers:

144

$\sqrt{90}$

Correct answer:

$\sqrt{90}$

Explanation:

To solve this problem, we are going to use the Pythagorean Theorom, which states that $a^{2}+b^{2}=c^{2}$ .

We know that this particular right triangle has a base of , which can be substituted for , and a height of , which can be substituted for . If we rewrite the theorom using these numbers, we get:

$3^{2}+9^{2}=c^{2}$

Next, we evaluate the expoenents:

$3^{2}=9$

$9^{2}=81$

$9+81=c^{2}$

9+81=90

Then, $90=c^{2}$ .

To solve for , we must find the square root of . Since this is not a perfect square, our answer is simply $c=\sqrt{90}$ .

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

What is the hypotenuse of a right triangle with sides 5 and 8?

Possible Answers:

100

$\sqrt{89}$

undefined

Correct answer:

$\sqrt{89}$

Explanation:

According to the Pythagorean Theorem, the equation for the hypotenuse of a right triangle is $a^{2} + b^{2}=c^{2}$ . Plugging in the sides, we get $5^{2}+8^{2}=c^{2}$ . Solving for , we find that the hypotenuse is $\sqrt{89}$ :

25+64=c^2

89=c^2

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Example Question #3 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

In a right triangle, two sides have length . Give the length of the hypotenuse in terms of .

Possible Answers:

$2\sqrt{3}t$

$\sqrt{2}t$

$2\sqrt{2}t$

$\sqrt{3}t$

Correct answer:

$2\sqrt{2}t$

Explanation:

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and side length.

$c^2=s^2+s^2\Rightarrow c^2=(2t)^2+(2t)^2\Rightarrow c^2=8t^2\Rightarrow c=\sqrt{8t^2}=2\sqrt{2}t$

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

In a right triangle, two sides have lengths 5 centimeters and 12 centimeters. Give the length of the hypotenuse.

Possible Answers:

$13\ cm$

$14\ cm$

$15\ cm$

$14.5\ cm$

$13.5\ cm$

Correct answer:

$13\ cm$

Explanation:

This triangle has two angles of 45 and 90 degrees, so the third angle must measure 45 degrees; this is therefore an isosceles right triangle.

By the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let hypotenuse and , lengths of the other two sides.

$c^2=a^2+b^2\Rightarrow c^2=5^2+12^2\Rightarrow c^2=25+144=169$

$\Rightarrow c=\sqrt{169}\Rightarrow c=13\ cm$

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

In a right triangle, the legs are 7 feet long and 12 feet long. How long is the hypotenuse?

Possible Answers:

193

$3\sqrt{19$

$\sqrt{193}$

Correct answer:

$\sqrt{193}$

Explanation:

The pythagorean theory should be used to solve this problem.

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

$7^{2}+12^{2}+=c^{2}$

$49+144=c^{2}$

$193=c^{2}$

$\sqrt{193}=c$

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Apply the Pythagorean Theorem to Determine Unknown Side Lengths in Right Triangles: CCSS.Math.Content.8.G.B.7

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #92 : Geometry

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Example Question #101 : Geometry

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #3 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All Common Core: 8th Grade Math Resources

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