If I have a rectangular yard with an area of 48 square meters. And I put a fence post every 2 meters around the perimeter of the yard. But I only have 14 fence post.

Question

What would be the dimensions for the yard?

Answer 1

Let's assume the length of the yard is L meters and the width is W meters.

The area of a rectangle is given by A = L * W. From the given information, we have A = 48 square meters.

The perimeter of a rectangle is given by P = 2L + 2W. We know that fence posts are placed every 2 meters along the perimeter, so the total number of fence posts required is equal to P/2 = L + W.

Given that you only have 14 fence posts, we can write the equation: L + W = 14.

Now, let's solve this system of equations.

1. From A = L * W, substitute A = 48:
48 = L * W --> equation (1)

2. From L + W = 14, solve for L:
L = 14 - W --> equation (2)

Substitute equation (2) into equation (1):
48 = (14 - W) * W
48 = 14W - W^2
0 = W^2 - 14W + 48
0 = (W - 6)(W - 8)

Now, we have two possible values for W: W = 6 or W = 8.

If W = 6, substitute this value into equation (2):
L = 14 - 6
L = 8

So, if the width is 6 meters and the length is 8 meters, the dimensions of the yard would be 8 meters by 6 meters, with an area of 48 square meters.

If W = 8, substitute this value into equation (2):
L = 14 - 8
L = 6

So, if the width is 8 meters and the length is 6 meters, the dimensions of the yard would still be 8 meters by 6 meters, with an area of 48 square meters.

Therefore, the dimensions of the yard would be 8 meters by 6 meters.