Plane Geometry - SSAT Middle Level Quantitative

The area of a rectangle can be found by multiplying the length by the width.

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.

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

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.

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

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

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

.

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.

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

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

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.

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.

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

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.

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.

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.

So, we can substitute. We get

The formula for the area of a triangle is .

Plug the given values into the formula to solve:

The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting :

Use the area formula for a triangle, setting :