Bunuel wrote:

The perimeter of a rectangular yard is completely surrounded by a fence that measures 40 meters. What is the length of the yard if the area of the yard is 64 meters squared?

A. 8

B. 10

C. 12

D. 14

E. 16

Let L = the length of the rectangle

Let W = the width of the rectangle

The perimeter is 40 meters.So, L + L + W + W = 40

Simplify: 2L + 2W = 40

Divide both sides by 2 to get:

L + W = 20The area is 64 square meters.So,

LW = 64We now have two equations.

First, if

L + W = 20, then W = 20 - L

Now take

LW = 64 and replace W with (20 - L) to get: L(20 - L) = 64

Expand to get: 20L - L² = 64

Rearrange to get: L² - 20L + 64 = 0

Factor: (L - 4)(L - 16) = 0

So, L = 4 or L = 16

So, it LOOKS like we have two different solutions. However, they are actually the SAME solution.

If L = 4, then W = 16

If L = 16, then W = 4

So, the dimensions of the rectangle are 4 X 16. So, we can say that the length is EITHER 4 or 16.

Since only 16 appears among the answer choices, the correct answer must be E

Cheers,

Brent

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