To solve, simply multiply width and length. Thus,

Based on the information given to you, you know that the area could be written as:

Likewise, you know that the perimeter is:

Now, isolate one of the values. For example, based on the second equation, you know:

Dividing everything by , you get:

Now, substitute this into the first equation:

To solve for , you need to isolate all of the variables on one side:

or:

Now, factor this:

, meaning that could be either or . These are the dimensions of your rectangle.

You could also get this answer by testing each of your options to see which one works for both the perimeter and the area.

To solve, simply use the formula for the area of a rectangle. Thus,

Since the width is twice the height, we know that the general area equation, which is

could be written:

Thus, we know:

or

This means that must be ; however, notice that the question asks for the length of the longer side. Thus, the answer is .

We know that the following represents the formula for the perimeter of a rectangle:

In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:

Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.

We also know that the length is two times the width; therefore, we can write the following:

The area of a rectangle is found by using this formula:

The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.

To find area, simply multiply length times width. Thus,

Because of complexities that arise with square units, it is best to start a problem like this by changing all of your units into inches from the very beginning. Thus, you know that the yard is or inches by or inches.

Thus, the area of the yard is

the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.

The area of the rectangle can be determined from multiplying length by width, so,

4 x 8 = 32 inches squared

First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.

The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in2.