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 ----
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
A=LW
its a square so L=W
so L=W
use distribution
L=4 or L=-20 since the length cant be negative L=4 and W=4
Answer by Theo(13342) (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.
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