The length of the rectangle garden is three feet less than twice its width. if the perimeter of the garden is 42 feet, what is its length? ( 10marks)

13 feet

Step-by-step explanation:

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