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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

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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