The dimensional of a rectangular garden were 4 m by 5 m. Each dimension was increased by the same amount. The garden then had an area of 56 m squared. Find the dimensions of the new garden. (hint let x be the amount of increase)

Question

Mathematics

Williamson

14 June, 11:03

The dimensional of a rectangular garden were 4 m by 5 m. Each dimension was increased by the same amount. The garden then had an area of 56 m squared. Find the dimensions of the new garden. (hint let x be the amount of increase)

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Answers (1)

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Beatrice Haas · Answer 1

w=4+x

l=5+x

A = l*w

substitute

56 = (4+x) * (5+x)

foil

56 = 20 + 4x+5x+x^2

56 = x^2 + 9x+20

subtract 56 from each side

0 = x^2 + 9x - 36

factor

0 = (x+12) (x-3)

x+12=0 x-3=0

x = - 12 x=3

x cannot be negative so x=3

new dimensions

w = 4+3 = 7

l=5+3 = 8

Answer: 7m by 8m