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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Example Questions

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Example Question #26 : Properties Of Triangles

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

Possible Answers:

Correct answer:

Explanation:

You need to use the Pythagorean Theorem, which is .

Add the first two values and you get . Take the square root of both sides and you get .

Example Question #27 : Properties Of Triangles

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

Possible Answers:

 units

 units

 units

 units

Correct answer:

 units

Explanation:

Using the numbers given to us by the question,

 units

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

A right triangle has legs with the lengths  and . Find the length of the hypotenuse.

Possible Answers:

Correct answer:

Explanation:

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

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.

12

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem to find the hypotenuse.

Example Question #12 : Triangles

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

Possible Answers:

Correct answer:

Explanation:

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

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 .


Next we evaluate the exponents:

Now we add them together:

Then, .

is not a perfect square, so we simply write the square root as  .

Example Question #13 : Triangles

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

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we are going to use the Pythagorean Theorom, which states that .

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:

Next, we evaluate the expoenents:

Then, .

To solve for , we must find the square root of . Since this is not a perfect square, our answer is simply .

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

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

Possible Answers:

undefined

Correct answer:

Explanation:

According to the Pythagorean Theorem, the equation for the hypotenuse of a right triangle is . Plugging in the sides, we get . Solving for , we find that the hypotenuse is :

Example Question #4 : 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:

Correct answer:

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.

Example Question #5 : 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 lengths 5 centimeters and 12 centimeters. Give the length of the hypotenuse.

Possible Answers:

Correct answer:

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.

Example Question #6 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

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

Possible Answers:

Correct answer:

Explanation:

The pythagorean theory should be used to solve this problem. 

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