### All ACT Math Resources

## 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:**

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

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

**Possible Answers:**

**Correct answer:**

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

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

Using the Pythagorean Theorem, we know that .

This gives:

Subtracting 9 from both sides of the equation gives:

inches

### Example Question #45 : Right Triangles

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

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

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

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

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

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

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

**Possible Answers:**

**Correct answer:**

### 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:**

**Correct answer:**

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

miles

**Possible Answers:**

**Correct answer:**