ACT Math : How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If the base of a right triangle is 5 cm long and the height of the triangle is 7 cm longer than the base, what is the length of the third side of the triangle in cm?

Possible Answers:

Correct answer:

Explanation:

Find the height of the triangle 

Use the Pythagorean Theorem to solve for the length of the third side, or hypotenuse.

 

Example Question #41 : Right Triangles

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Given the right triangle in the diagram, what is the length of the hypotenuse?

 

Possible Answers:

Correct answer:

Explanation:

To find the length of the hypotenuse use the Pythagorean Theorem:

 Where  and  are the legs of the triangle, and  is the hypotenuse.

The hypotenuse is 10 inches long.

 

Example Question #44 : Right Triangles

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 3 inches and C = 5 inches, what is the length of side B?  

Possible Answers:

1/2 inches

1 inches

4 inches

6 inches

4.5 inches

Correct answer:

4 inches

Explanation:

Using the Pythagorean Theorem, we know that .

This gives: 

Subtracting 9 from both sides of the equation gives: 

 inches

 

Righttriangle

Example Question #45 : Right Triangles

Righttriangle

Triangle ABC is a right triangle. If the length of side A = 8 inches and B = 11 inches, find the length of the hypoteneuse (to the nearest tenth). 

Possible Answers:

13.7 inches

14.2 inches

185 inches

13.6 inches

184 inches

Correct answer:

13.6 inches

Explanation:

Using the Pythagrean Theorem, we know that .

This tells us:

Taking the square root of both sides, we find that  inches

Example Question #46 : Right Triangles

Righttriangle

Given:

A = 6 feet

B = 9 feet

What is the length of the hypoteneuse of the triangle (to the nearest tenth)?

Possible Answers:

10.8 feet

10.2 feet

10.5 feet

10.6 feet

10.1 feet

Correct answer:

10.8 feet

Explanation:

Using the Pythagrean Theorem, we know that .

This tells us:

Taking the square root of both sides, we find that 

Example Question #47 : Right Triangles

Righttriangle

Given:

A = 2 miles

B = 3 miles

What is the length of the hypoteneuse of triangle ABC, to the nearest tenth? 

Possible Answers:

3.2 miles

3.6 miles

3.5 miles

3.7 miles

3.4 miles

Correct answer:

3.6 miles

Explanation:

Using the Pythagrean Theorem, we know that .

This tells us:

Taking the square root of both sides, we find that 

Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Given that two sides of a right triangle measure 2 feet and 3 feet, respectively, with a hypoteneuse of x, what is the perimeter of this right triangle (to the nearest tenth)?

Possible Answers:

3.6 feet

8.6 feet

6.4 feet

9.4 feet

18 feet

Correct answer:

8.6 feet

Explanation:

Using the Pythagrean Theorem, we know that .

This tells us:

Taking the square root of both sides, we find that 

To find the perimeter, we add the side lengths together, which gives us that the perimeter is: 

Example Question #22 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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Possible Answers:

Correct answer:

Explanation:

Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel? 

Possible Answers:

\dpi{100} \small 14\ miles

\dpi{100} \small 10\ miles

\dpi{100} \small 8\ miles

\dpi{100} \small 16\ miles

\dpi{100} \small 12\ miles

Correct answer:

\dpi{100} \small 10\ miles

Explanation:

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

  \dpi{100} \small 6^{2}+8^{2}=x^{2}

\dpi{100} \small 36+64=x^{2} 

\dpi{100} \small x=10 miles

Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Possible Answers:

Correct answer:

Explanation:

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