Asked by Michelle
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
A)
340
B)
74
C)
135
D)
900
Answers
Answered by
Reiny
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
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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