### All ACT Math Resources

## Example Questions

### Example Question #57 : Right Triangles

Paul leaves his home and jogs 3 miles due north and 4 miles due west. If Paul could walk a straight line from his current position back to his house, how far, in miles, is Paul from home?

**Possible Answers:**

7

5

25

4

√14

**Correct answer:**

5

By using the Pythagorean Theorem, we can solve for the distance “as the crow flies” from Paul to his home:

3^{2} + 4^{2} = *x*^{2}

9 + 16 = *x*^{2}

25 = *x*^{2}

5 = *x*

### Example Question #58 : Right Triangles

Given a right triangle where the two legs have lengths of 3 and 4 respectively, what is the length of the hypotenuse?

**Possible Answers:**

5

25

9

4

3

**Correct answer:**

5

The hypotenuse can be found using Pythagorean Theorem, which is a^{2 }+ b^{2 }= c^{2}, so we plug in a = 3 and b = 4 to get c.

c^{2 }=25, so c = 5

### Example Question #59 : Right Triangles

Length *AB* = 4

Length *BC* = 3

If a similar triangle has a hypotenuse length of 25, what are the lengths of its two legs?

**Possible Answers:**

20 and 25

15 and 25

5 and 25

15 and 20

3 and 4

**Correct answer:**

15 and 20

Similar triangles are in proportion.

Use Pythagorean Theorem to solve for *AC*:

Pythagorean Theorem: *AB*^{2} + *BC*^{2} = *AC*^{2}

4^{2} + 3^{2} = *AC*^{2}

16 + 9 = *AC*^{2}

25 = *AC*^{2}

*AC* = 5

If the similar triangle's hypotenuse is 25, then the proportion of the sides is *AC*/25 or 5/25 or 1/5.

Two legs then are 5 times longer than *AB* or *BC*:

5 * (*AB*) = 5 * (4) = 20

5 * (*BC*) = 5 * (3) = 15

### Example Question #61 : Right Triangles

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 #62 : 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 #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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:**

4.5 inches

1 inches

6 inches

4 inches

1/2 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 #64 : 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

185 inches

184 inches

14.2 inches

13.6 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 #65 : 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:**

10.5 feet

10.8 feet

10.6 feet

10.1 feet

10.2 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 #66 : 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:**

3.6 miles

3.5 miles

3.7 miles

3.4 miles

3.2 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 #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:**

3.6 feet

8.6 feet

18 feet

6.4 feet

9.4 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:

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