Find the area of a rectangle with a perimeter of 32 if its length is two larger than its width. Round to the nearest tenth if necessary.

Question

How? Help please.

Answer 1

We first need to find the length and width of the sides, which we can do knowing that length = width * 2.  If we use the known perimeter, we can quickly determine the length and width:

 

P = 2L + 2W

32 = 2L + 2W

Since L = 2W, we can substitute:

32 = 2(2W) + 2W

32 = 4W + 2W

32 = 6W

W = 5.333

(2)W = (2)5.333

2W = 10.666

Since L = 2W, we can substitute:

L = 10.666

 

Now, we know that the length is 10.666 and width is 5.333.  We use the basic area formula to solve:

 

A = L * W

A = 10.666 * 5.333

A = 56.9 (rounded to nearest tenth)