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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