### All High School Math Resources

## Example Questions

### Example Question #1 : Right Triangles

Solve for (rounded to the nearest tenth). Figure not drawn to scale.

**Possible Answers:**

**Correct answer:**

We will use the Pythagorean Theorem to solve for the missing side length.

### Example Question #2 : Right Triangles

A square boxing ring has a perimeter of feet. When the two boxers are sitting in opposite corners between rounds, how far apart are they?

**Possible Answers:**

feet

feet

feet

feet

feet

**Correct answer:**

feet

Since the perimeter of the ring is feet and the ring is a square, solve for the length of a single side of the ring by dividing by .

The distance between the two boxers in opposing corners is a straight line from any one corner to the other. That straight line forms the hypotenuse of a right triangle whose other two sides are each feet long (since they are each the sides of the square).

Solving for the length of the hypotenuse of this right triangle with the pythagorean theorem provides the distance between the two boxers when they are in opposite corners.

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

Given a right triangle with a leg length of 6 and a hypotenuse length of 10, find the length of the other leg, *x*.

**Possible Answers:**

64

16

4

8

**Correct answer:**

8

Using Pythagorean Theorem, we can solve for the length of leg *x*:

*x*^{2} + 6^{2} = 10^{2}

Now we solve for *x*:

*x*^{2} + 36 = 100

*x*^{2} = 100 – 36

*x*^{2} = 64

*x* = 8

Also note that this is proportionally a 3/4/5 right triangle, which is very common. Always look out for a side-to-hypoteneuse ratio of 3/5 or 4/5, or a side-to-side ratio of 3/4, in any right triangle, so that you may solve such triangles rapidly.

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

In a right triangle a hypotenuse has a length of 8 and leg has a length of 7. What is the length of the third side to the nearest tenth?

**Possible Answers:**

**Correct answer:**3.9

Using the pythagorean theorem, 8^{2}=7^{2}+x^{2}. Solving for x yields the square root of 15, which is 3.9^{}

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

Given a right triangle with a leg length of 2 and a hypotenuse length of √8, find the length of the other leg, *x*.

**Possible Answers:**

10

√8

2

6

4

**Correct answer:**

2

Using Pythagorean Theorem, we can solve for the length of leg *x*:

*x*^{2} + 2^{2} = (√8)^{2 }= 8

Now we solve for *x*:

*x*^{2} + 4 = 8

*x*^{2} = 8 – 4

*x*^{2} = 4

*x* = 2

### Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

The legs of a right triangle are and . Rounded to the nearest whole number, what is the length of the hypotenuse?

**Possible Answers:**

**Correct answer:**

Use the Pythagorean Theorem. The sum of both legs squared equals the hypotenuse squared.

### Example Question #3 : Right Triangles

**Possible Answers:**

**Correct answer:**

Use the Pythagorean theorem: .

We know the length of one side and the hypotenuse.

Now we can solve for the missing side.

### 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:**

9

12

171

14.87

13.07

**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 #1 : 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

12, 16, 20

5, 7, 10

8, 15, 17

5, 12, 13

**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:**

10, 12, 16

6, 7, 8

9, 12, 15

4, 6, 9

**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.