The length of Hallie's garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. What are the dimensions of Hallie's garden?

A. 7 meters and 3 meters

B. 13 meters by 3 meters

C. 17 meters and 55 meters

D. 28 meters by 8 meters

Answer: The correct answer is D; 28 meters by 8 meters

Step-by-step explanation: The first thing we can see from the question is that Hallie's garden is rectangular in shape, since the length and the width are of different dimensions. So we shall call the length L, and we shall call the width W.

Now we have been told that the length is 4 meters greater than the width. What this implies is that if the width is W, then the length is going to be 3W + 4. This is because the question clearly states that the length is 4 meters greater than 3 times the width. Three times the width can be expressed as 3 x W (or 3W) and four meters greater than this can be further expressed as

3W + 4.

Therefore the length is 3W + 4 and the width is W. If the perimeter is given as 72 meters, then we can use that bit of information to derive the length and the width

Perimeter = 2 (L + W) can be re-written as

Perimeter = 2 ({3W + 4} + W)

(We have just inserted the new values of the length and the width)

72 = 2 (3W + 4 + W)

72 = 2 (4W + 4)

72 = 8W + 8

Subtract 8 from both sides of the equation

72 - 8 = 8W + 8 - 8

64 = 8W

Divide both sides of the equation by 8

8 = W

Now we have computed the width to be 8 meters, we use this to calculate the value of the length which is L. Remember that L, in this question is given as 3W + 4. If W is 8, then

L = 3 (8) + 4

L = 24 + 4

L = 28

Hence, the length is 28 meters and the width is 8 meters.