SOLUTION: If the sides of a square are lenghtened by 8 cm, the area becomes 144cm^2, find the length of a side of the original square, The length of a side of the original square is ----

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Question 285611: If the sides of a square are lenghtened by 8 cm, the area
becomes 144cm^2, find the length of a side of the original square,
The length of a side of the original square is ------- cm.
Found 2 solutions by JBarnum, Theo:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
A=LW
its a square so L=W
so %28L%2B8%29%28W%2B8%29=144 L=W
%28L%2B8%29%28L%2B8%29=144use distribution
L%5E2%2B8L%2B8L%2B64=144
L%5E2%2B16L-80=0
%28L-4%29%28L%2B20%29=0
L=4 or L=-20 since the length cant be negative L=4 and W=4

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
formula for area of a square is:

a = x^2

Increase the side by 8 cm and the formula becomes:

144 = (x+8)^2

You want to find the length of the side of the original square, which is x.

(x+8)^2 = x^2 + 16x + 64

Equation becomes:

144 = x^2 + 16x + 64

Subtract 144 from both sides of this equation to get

0 = x^2 + 16x - 80

This factors out to be:

0 = (x+20) * (x-4)

You get x = -20 or x = 4

x can't be negative so x has to be 4.

When x = 4, the area is 4^2 = 16
When x = 4 + 8 = 12, the area is 12^2 = 144

Numbers check out so answer is that the side of the original square is 4 cm.