Question 176986: if the two sides of a rectangle change so that the area remains constant,and one side is increased by 25%,what percentage increse or decrease of the other side.
Answer by colliefan(242)   (Show Source):
You can put this solution on YOUR website! Area is length x width.
Say it is the width that is increased by 25%.
Then the new width is w plus 25% of w or w + 25%w or 125%w or {125/100 w} or {5/4 w}
Then, the new area is A = 5/4 w * l
But we know that the new area must equal the old area. If the width has increased, the length must decrease so the area is the same. The width has increased by 5/4. That is the fraction that must be "cancelled out" so that the area doesn't change. The L must be decreased by the fraction that cancels out the 5/4, that is 4/5.
A = (5/4 * w) * (4/5 * l)
A = 5/4 * 4/5 * w * l
A = 1 * w * l
A = w * l
Thus, the original Area is the same if the length is 4/5 the original or is 80% of the original or is decreased by 20%.
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