### All SSAT Middle Level Math Resources

## Example Questions

### Example Question #1 : How To Find Perimeter Of A Triangle

The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?

**Possible Answers:**

**Correct answer:**

Since it is isosceles, 2 of the sides must be equal. They must also add to 18.

### Example Question #2 : How To Find Perimeter Of A Triangle

An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?

**Possible Answers:**

2 feet 6 inches

2 feet 10 inches

3 feet 2 inches

2 feet 2 inches

3 feet 4 inches

**Correct answer:**

2 feet 10 inches

One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to inches.

An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:

To convert 34 inches to feet and inches:

One side measures 2 feet 10 inches.

### Example Question #1 : Perimeter Of A Triangle

Find the perimeter of the triangle above.

*Note: Figure not drawn to scale.*

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: .

Because the lengths are in inches, the answer must be in inches as well.

### Example Question #1 : How To Find Perimeter Of A Triangle

If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?

**Possible Answers:**

21

15

20

12

19

**Correct answer:**

19

An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.

### Example Question #62 : Geometry

The perimeter of equilateral triangle *QRS* is 4 times the perimeter of equilateral triangle *TUV*. If the perimeter of *QRS* is 36, what is the length of one side of *TUV?*

**Possible Answers:**

9

12

3

4

18

**Correct answer:**

3

If the perimeter of *QRS* is 4 times the perimeter of *TUV,* and the perimeter of *QRS *is 36, then the perimeter of *TUV* is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle *TUV* is 9, then each individual side must have length 3.

### Example Question #1 : How To Find Perimeter Of A Triangle

What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?

**Possible Answers:**

**Correct answer:**

Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.

In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.

Add the sides together to find the total perimeter.

The perimeter of the triangle is 9 feet.

### Example Question #1 : How To Find Perimeter Of A Triangle

The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?

**Possible Answers:**

**Correct answer:**

Since the triangle is an isoscles, two of the sides must be equal. They must also add to . Looking at the possibilities, only have two sides that are the same length. Now we need to check the triangle inequality to make sure the lengths create a triangle. The triangle inequality is:

Plugging into these inequalities we get:

Therefore, the inequalities hold true thus, creates a triangle. Now we need to look at the sum of the lengths:

Therefore, is the correct answer.

### Example Question #1 : Geometry

A triangle has sides feet, feet, and feet. Calculate its perimeter.

**Possible Answers:**

**Correct answer:**

The perimeter of any figure is the sum of the lengths of the sides: .

### Example Question #8 : How To Find Perimeter Of A Triangle

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

**Possible Answers:**

**Correct answer:**

By the Pythagorean Theorem, if and are the legs of a right triangle and is its hypotenuse, then

.

Set and solve for :

The perimeter of the triangle - the sum of the sidelengths - is

.

### Example Question #71 : Geometry

What is the perimeter of an equilateral triangle with a side length ?

**Possible Answers:**

**Correct answer:**

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

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