How to find perimeter of a triangle

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SSAT Middle Level Quantitative › How to find perimeter of a triangle

Questions 1 - 10
1

Q_5

Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

None of these answers are correct.

Explanation

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.

2

Find the perimeter of a triangle with sides , , and .

Explanation

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals . Therefore, the answer is .

3

A right triangle has legs feet and feet long. What is its perimeter, in inches?

Explanation

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute :

feet

Its perimeter is feet. Multiply by 12 to get the perimeter in inches:

inches

4

Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?

Explanation

An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.

This makes the perimeter either

or

Of our choices, we choose 38.

5

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

Explanation

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.

6

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

Explanation

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.

7

An equilateral triangle has perimeter centimeters. How long is one side?

Explanation

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

8

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

Explanation

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

.

9

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

Explanation

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

10

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

Explanation

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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