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- anonymous

if the sides of a square are lengthened by 8 cm, the area becomes 256 cm^2, find the legth of the origional side

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- mathteacher1729

A square has four equal sides, and if each side is of length x, that means the area is x^2. Now, you make each side 8cm longer, so that means each side of the square is now (x+8) and the area is (x+8)^2 or (x+8)(x+8).
Since the new area is 256 that means....
(x+8)(x+8)=256
Expand the expression on the left to reveal a quadratic equation, and solve. :)

- anonymous

12?

- mathteacher1729

No. If the original side were 12, that means the new sides are 20. 20*20 = 400 . That's too big.

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- mathteacher1729

Question -- "what number , when you square it, is 256?"

- anonymous

16?

- anonymous

thats even bigger

- anonymous

8; the new area is 256, take the square root to get 16 for new length of each side. Since the new side is 16 and the old side was 8 less, the old square was 8 [16-8=8)

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