One side of the rectangle was doubled, and the other was reduced by 30 percent.

univerkov | May 29, 2021 | education

One side of the rectangle was doubled, and the other was reduced by 30 percent. Has its area increased or decreased, by what percentage?

Let us denote the length of side number one of a given rectangular quadrangle by a, and the length of side number two of a given rectangular quadrilateral by b.

Then the area of this rectangular quadrangle will be a * b.

If side number one of this rectangular quadrangle is doubled, and the other is reduced by 3 tens of percent, then the length of side number one will be 2a, and the length of side number two will be b – (30/100) * b = b – (3/10) * b = b – 0.3 * b = 0.7 * b, and the area of the resulting rectangle will be 2a * 0.7 * b = 1.4 * a * b.

Therefore, the area of the original quadrangle will increase by:

100 * (1.4 * a * b – a * b) / (a * b) = 100 * 0.4 * a * b / (a * b) = = 100 * 0.4 = 40%.

Answer: the area will increase by 40%.

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