Question 177086
The area of the original rectangle is *[tex \large A = xy\]


If you increase the size of side *[tex \large x\] by 25%, then the new side is *[tex \large 1.25x\] and in order for the area to remain the same, the other side of the rectangle has to be multiplied by some factor we can call *[tex \large r\], making the new side *[tex \large ry\].  So the area of the new rectangle is *[tex \large A = (1.25x)(ry)]


But we are given that the two rectangles have the same area, so:


*[tex \large xy = (1.25x)(ry)\]


Divide both sides of this equation by *[tex \large xy\] and we have:


*[tex \large 1 = 1.25r \text{ }\Rightarrow\text{ } r = \frac{1}{1.25} = .8\]


Which is to say that the other side is decreased by *[tex \large 1 - 0.8 = 0.2 = 20%]