Question 1092588
let x equal the original length of the side of the square.
let y equal the new length of the side of the square.


you get x/y = 4/5


cross multiply to get 5x = 4y


solve for y to get y = 5x/4 = 5/4 * x


5/4 * x is equivalent to (4/4 + 1/4) * x which is equal to 1 * x + 1/4 * x.


the original length of the side is increased by 1/4 * the length of the original side.


that would be equal to 25% of the length of the original side.


another way of getting to the same answer is:


y = 5/4 * x = 1.25 * x


increase percent is equal to (1.25 * x - x) / x = .25.


multiply that by 100 to 25%.


assume the original length of the side is 100.


increase that by 25% and the length of the new side is 125.


the ratio of the original length to the new length is 100 / 125 which simplifies to 4/5 when you divide both numerator and denominator by 25.