SOLUTION: 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.

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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