Question

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)

Answer 1

Answer:

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

Answer 2

The length will be 13 feet.

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

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