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Robert has a rectangular garden that is currently 180ft^2 and has a perimeter of 54ft He wants to increase the size of his garden by 5 ft in both directions. What will be the area of his expanded garden?

A)
340
B)
74
C)
135
D)
900

let the width be x
let the length be y

so we know 2x + 2y = 54
x + y = 27
and y = 27-x

new width = x+5
new length = y+5 = 27-x + 5 = 32-x

Isn't area = length x width ?
old garden:
x(27-x) = 180
-x^2 + 27x - 180 = 0
x^2 - 27x + 180 = 0
(x-15)(x-12) = 0
x = 15 or x = 12
then y = 12 or y = 15 (symmetric solution)

so the garden was 15 by 12

take it from there

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