By how many percent and how has the area of the rectangle changed, if one side

| March 15, 2021 | education

By how many percent and how has the area of the rectangle changed, if one side of the rectangle was increased: by 50%, and the other was reduced by 50%?

Let us denote the lengths of the sides of this rectangle through x and y.

Then the area S of this rectangle will be:

S1 = x * y.

If the first side of this rectangle is increased by 50%, and the second side of this rectangle is reduced by 50%, then the first side of the rectangle will be x + (50/100) x = 1.5x, and the second rectangle will be y – (50/100) y = 0.5y.

Then the area S2 of the resulting rectangle will be:

S2 = 1.5x * 0.5y = 0.75xy = 0.75 * S1.

Therefore, the area of ​​the original rectangle will decrease by:

100 * (S1 – 0.75 * S1) / S1 = 100 * 0.25 * S1 / S1 = 100 * 0.25 = 25%.

Answer: the area of ​​the rectangle will decrease by 25%.



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