### All PSAT Math Resources

## Example Questions

### Example Question #131 : Plane Geometry

Note: Figure NOT drawn to scale.

Refer to the above figure. Given that , give the area of .

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

By the Pythagorean Theorem,

The similarity ratio of to is

,

This can be used to find :

The area of is therefore

### Example Question #1 : Right Triangles

Note: Figures NOT drawn to scale.

Refer to the above figure. Given that , evaluate .

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem, since is the hypotenuse of a right triangle with legs 6 and 8, its measure is

.

The similarity ratio of to is

.

Likewise,

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:

**Possible Answers:**

12

14.87

13.07

9

171

**Correct answer:**

13.07

The Pythagorean Theorem gives us *a*^{2} + *b*^{2} = *c*^{2} for a right triangle, where *c* is the hypotenuse and *a* and *b* are the smaller sides. Here *a* is equal to 5 and *c* is equal to 14, so *b*^{2} = 14^{2} – 5^{2} = 171. Therefore *b* is equal to the square root of 171 or approximately 13.07.

### Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Which of the following could NOT be the lengths of the sides of a right triangle?

**Possible Answers:**

14, 48, 50

5, 12, 13

8, 15, 17

5, 7, 10

12, 16, 20

**Correct answer:**

5, 7, 10

We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.

All of the other answer choices observe the theorem *a*^{2} + *b*^{2} = *c*^{2}

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Which set of sides could make a right triangle?

**Possible Answers:**

4, 6, 9

9, 12, 15

10, 12, 16

6, 7, 8

**Correct answer:**

9, 12, 15

By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.

**Possible Answers:**

4

4.5

3.5

5

5.5

**Correct answer:**

4

Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗^{2 }–〖12〗^{2}) = 9, so x=9 – 5=4

### Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has sides of 36 and 39(hypotenuse). Find the length of the third side

**Possible Answers:**

42

15

33

12 √6

33√2

**Correct answer:**

15

use the pythagorean theorem:

a^{2} + b^{2} = c^{2} ; a and b are sides, c is the hypotenuse

a^{2} + 1296 = 1521

a^{2} = 225

a = 15

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?

**Possible Answers:**

2 hours and 30 minutes

3 minutes and 50 seconds

1 hour and 45 minutes

4 hours and 0 minutes

3 minutes and 20 seconds

**Correct answer:**

3 minutes and 20 seconds

Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has two sides, 9 and *x*, and a hypotenuse of 15. What is *x*?

**Possible Answers:**

10

12

11

13

14

**Correct answer:**

12

We can use the Pythagorean Theorem to solve for *x*.

9^{2} + *x*^{2} = 15^{2}

81 + *x*^{2} = 225

*x*^{2} = 144

*x* = 12

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?

**Possible Answers:**

**Correct answer:**

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