SOLUTION: Terry has a square patio. After expanding the length by 20 ft and the width by 10 ft the areas was 999 ft^2, what was the original area?

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Question 825096: Terry has a square patio. After expanding the length by 20 ft and the width by 10 ft the areas was 999 ft^2, what was the original area?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
w is side length of the original square.

highlight_green%28%28w%2B20%29%28w%2B10%29=999%29
w%5E2%2B20w%2B30w%2B200=999
w%5E2%2B50w=799
w%5E2%2B50w-799=0
'
w=%28-50%2Bsqrt%282500%2B4%2A799%29%29%2F%282%29
w=%28-50%2Bsqrt%282500%2B3196%29%29%2F2
w=%28-50%2Bsqrt%285696%29%29%2F2

5695=4*1424=4*2*712=4*4*356=4*4*4*89, 89 is prime
w=%28-50%2B8%2Asqrt%2889%29%29%2F2
highlight%28w=-25%2B4%2Asqrt%2889%29%29
That is the side length of the original square. Raise to the power of 2, and you get the area.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Terry has a square patio. After expanding the length by 20 ft and the width by 10 ft the areas was 999 ft^2, what was the original area? 


One side of original square = 17

Area of original square  = 17%5E2, or highlight_green%28289ft%5E2%29

You can do the check!! 



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