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

Study concepts, example questions & explanations for SAT Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

Example Question #481 : Psat Mathematics

Screen_shot_2013-09-16_at_11.16.22_am

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 #41 : 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:

6 inches

4 inches

1/2 inches

1 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 #64 : 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:

14.2 inches

184 inches

185 inches

13.6 inches

13.7 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 #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Righttriangle

Given:

A = 6 feet

B = 9 feet

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

Possible Answers:

10.1 feet

10.2 feet

10.6 feet

10.8 feet

10.5 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 #22 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Righttriangle

Given:

A = 2 miles

B = 3 miles

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

Possible Answers:

3.5 miles

3.4 miles

3.7 miles

3.2 miles

3.6 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 #67 : Right Triangles

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:

8.6 feet

9.4 feet

3.6 feet

18 feet

6.4 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 #101 : Geometry

Img052

Possible Answers:

Correct answer:

Explanation:

Example Question #23 : 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 8\ miles

\dpi{100} \small 12\ miles

\dpi{100} \small 16\ miles

\dpi{100} \small 10\ 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 #69 : Right Triangles

Possible Answers:

Correct answer:

Explanation:

Example Question #24 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east.  What is the straight line distance from Jeff’s work to his home?

 

 

Possible Answers:

10√2

2√5

15

11

6√2

Correct answer:

10√2

Explanation:

Jeff drives a total of 10 miles north and 10 miles east.  Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated.  102+102=c2.  200=c2. √200=c. √100Ÿ√2=c. 10√2=c

Learning Tools by Varsity Tutors