Setup and answer

## The perimeter of a rectangle is 42. Meters. The length of the rectangle is three meters less than twice the width. Find the dimensions of the rectangle

# 2 Answers

You are given that the perimeter, P, of the rectangle is 42 meters (i.e., P = 42). Also, the length, L, of the rectangle is 3 meters less than 2 times the width, W (i.e., L = 2W - 3).

Recall that the perimeter, P, of a rectangle is given by the following formula:

P = 2W + 2L

Substituting 2W - 3 for L, we arrive at the following:

P = 2W + 2(2W - 3)

P = 2W + 2·2W + 2·-3

P = 2W + 4W - 6

P = 6W - 6

Since we were given that P = 42, then

42 = 6W - 6

42 + 6 = 6W - 6 + 6

48 = 6W

48/6 = 6W/6

8 = W

Therefore, the width of the rectangle is 8 meters. Use this value to solve for the length:

L = 2W - 3

L = 2·8 - 3

L = 16 - 3

L = 13

Therefore, the length of the rectangle is 13 meters.

Thus, the dimensions of the rectangle is length (in meters) X width (in meters), which we found to be:

13 meters X 8 meters

Perimeter of rectangle is P = 2(l + w)

l = 2w - 3 ---> 2((2w - 3) + w) = 42 ---> 2w - 3 + w = 21

---> 3w = 21 + 3 ---> w = 24/3 ---> **w = 8 meters**

l = 2 · 8 - 3 ---> **l = 13 meters**

2(13 + 8) = 42