SOLUTION: How do I find the length of the sides of the original square? If each side of a square is increased by 10cm. The area of the resulting square is 9 times the area of the original

Question 4707:
How do I find the length of the sides of the original square? If each side of a square is increased by 10cm. The area of the resulting square is 9 times the area of the original square.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The original area of the square is:
A = s^2 After increasing the sides by 10 cm, the new area is:
9A = (s+10)^2
9A = s^2 + 20s + 100 Substitute the A = s^2
9s^2 = s^2 + 20 s + 100
8s^2 - 20s - 100 = 0 Divide through by 4 then Solve by factoring.
2s^2 - 5s - 25 = 0 Factor.
(2s + 5)(s - 5) = 0 Apply the zero products principle.
2s + 5 = 0; 2s = -5 Discard this as negative lengths are not meaningful.
s - 5 = 0; s = 5
Original length of the sides of the square = 5 cm.
Check:
Original area: A = s^2 = 5^2 = 25 cm^2
New area = 9(25) = 225 cm^2;
(5 + 10)^2 = 15^2 = 225 cm^2

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