SOLUTION: if the sides of a square are lenghtened by 8cm, the area becomes 225cm<sup>2</sup>.Find the lenght of a side of the original square

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Question 325398: if the sides of a square are lenghtened by 8cm, the area becomes 225cm2.Find the lenght of a side of the original square
Found 2 solutions by checkley77, Edwin McCravy:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(X+8)^2=225
X^2+16X+64-225=0
X^2+16X-161=0
(X=23)(X-7)=0
X-7=0
X=7 cm. was the original square sides.
Proof:
(7+8)^2=225
15^2=225
225=225

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

We start with this square which has sides the unknown x:



Now let's add 8 cm to each side:



Now each side of the big square has length of side x plus the 8cm
we have added on.

So each side of the big square is x+8 cm.

Now we use the formula for the area of a square:

Area%22%22=%22%22%28one_side%29%5E2

We are told 

>>...area becomes 225cm2...<<

So we substitute 225 for A and (x+8) for "one side"

225%22%22=%22%22%28x%2B8%29%5E2

%28x%2B8%29%5E2%22%22=%22%22225

Take square roots of both side:

sqrt%28%28x%2B8%29%5E2%29%22%22=%22%22sqrt%28225%29

x%2B8%22%22=%22%2215

x%22%22=%22%227

So each side of the original square had length 7 cm.

Edwin