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04-01-2020
Mathematics

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A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing is are used, what is the maximum area that can be enclosed?
A: 9/2 m^2

B:81/4 m^2

C: 27 m^2

D: 40 m ^2

E: 81/2 m^2

Respuesta :

04-01-2020

Option E is the correct answer.

Explanation:

Let L be the length and W be the width.

We have only 2 sides are fenced

Fencing = 2L + W

Fencing = 18 m

2L + W = 18

W = 18 - 2L

We need to find what is the largest area that can be enclosed.

Area = Length x Width

A = LW

A = L x (18-2L) = 18 L - 2L²

For maximum area differential is zero

So we have

dA = 0

18 - 4 L = 0

L = 4.5 m

W = 18 - 2 x 4.5 = 9 m

Area = 9 x 4.5 = 40.5 m² = 81/2 m²

Option E is the correct answer.

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