SOLUTION: I have a space that is 9 ft long and 6 ft wide. I want to increase the dimensions of the space by the same distance each way and have the area of the new space 5 times the area of

Question 332210: I have a space that is 9 ft long and 6 ft wide. I want to increase the dimensions of the space by the same distance each way and have the area of the new space 5 times the area of the present space. How many ft should I add to both the width and the length? Thanks
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
length = 9 ft
width = 6 ft.
..
area = 9*6 = 54sq.ft
..
increase length & width by same amount = x
length = (x+9)
width = (x+6)
new area = (x+6)(x+9)
new area = 5 * present area
(x+6)(x+9)=5*54
x^2+15x+54=5*54
x^2+15x+54-270=0
x^2+15x-216=0
x^2+24x-9x-216=0
x(x+24)-9(x+24)=0
(x+24)(x-9)=0
x=9 feet has to be added to length & width
the new dimensions will be 18 by 15 feet.
CHECK
18*15= 5*54
270=270
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