SOLUTION: if the two sides of a rectangle change so that the area remains constant,and one side is increased by 25%,what is the percentage increase or decrease of the other side. i think i a

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if the sides are x and y, then the area is xy

let's increase x by 25%, so it is now 1.25x

if k is the change in y, then (1.25x)(ky)=xy

1.25kxy=xy

dividing by xy __ 1.25k=1

dividing by 1.25 __ k=.8 or 80%

so if one dimension is increased by 25%, the other dimension is DECREASED by 20% to keep the area constant

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The area of the original rectangle is

If you increase the size of side by 25%, then the new side is 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 , making the new side . So the area of the new rectangle is

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



Divide both sides of this equation by and we have:



Which is to say that the other side is decreased by