SOLUTION: The sides of a square were extended to form a rectangle 8cm longer and 3cm wider than the square. The area of the rectangle is 204 sq cm. What was the area of the original square?

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Question 639958: The sides of a square were extended to form a rectangle 8cm longer and 3cm wider than the square. The area of the rectangle is 204 sq cm. What was the area of the original square?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
We start with an x cm by x cm square



Then we extend it by 8 cm horizontally and 3 cm vertically, and
have this:



So the length of the extended rectangle is x+8 and the width is x+3

     Area = (length)(width)
      204 = (x+8)(x+3)
      204 = x²+3x+8x+24
      204 = x²+11x+24
Get 0 on the left
        0 = x²+11x-180
        0 = (x-9)(x+20)
Use zero factor property:
           x-9=0  x+20=0
             x=9     x=-20

Discard the negative answer.

Each side of the original square is 9 cm.

So the area of the original square is

     Area = (length)(width)
     Area = (9)(9)
     Area = 81 sq.cm.

Edwin