The width of the rectangle is w, therefore the length is 3w.  The perimeter, P, can then be described as P = w + w + 3w +3w

                                                                                          40 = 8w

                                                                                          w = 5

                                                                                          width = 5, length = 3w = 15

                                                                                          A = 5*15 = 75 square inches

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 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

96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches.  This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio.  She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.

Perimeter:  Sum of the sides:

4x + 4x + 2x+8 +2x+8 = 160

12x + 6 = 160

12x = 154

x =

Therefore, the short side of the rectangle is going to be:

And the long side is going to be:

The area of the rectangle is going to be as follows:

Area = lw

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.

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 .

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  

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

To solve, simply multiply width and length. Thus,