Question 1108173: If the length of each side of a square is doubled, the area is increased by 1875 inch squared. Find the length of each side of the original square.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! area of a square is equal to s^2, where s represents the length of a side.
if you let x = the area of the square, then the formula becomes s^2 = x.
if you double the length of the side of the square, then the length of the side of the square becomes 2s.
the area becomes (2s)^2 = 4s^2.
when you double the length of the square, the area is increased by 1875 square inches.
you get 4s^2 = x + 1875
so, you have s^2 = x and 4s^2 = x + 1875.
in the equation 4s^2 = x + 1875, replace s^2 by x, because s^2 = x, to get:
4x = x + 1875.
subtract x from both sides of this equation to get:
3x = 1875.
solve for x to get x = 625.
since x represents the area of the original square, then x = 625 square inches.
the length of the side of that square would be sqrt(625) = 25 inches.
if you double the length of the side of the original square, then the length becomes 50.
the area of that square becomes 50^2 = 2500 square inches.
2500 - 625 = 1875 square inches additional.
your solution is that the length of each side of the original square is 25 inches.
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