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## 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

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