The sides of the rectangle are 20 cm and 10 cm. One side is enlarged by 20% and the other is reduced by 20%.

| March 1, 2021 | education

The sides of the rectangle are 20 cm and 10 cm. One side is enlarged by 20% and the other is reduced by 20%. Has the area of the rectangle increased or decreased, and by what percentage? Does it matter which side is enlarged and which side is reduced? Justify the answer by solving the problem in general terms.

1. Let a1 and b1 be the sides of the rectangle.

2. After increasing the side a1 by 20%, we get:

a2 = a1 + a1 * 20% / 100% = a1 + 0.2a1 = 1.2a1.

3. After reducing the side b1 by 20%, we get:

b2 = b1 – b1 * 20% / 100% = b1 – 0.2b1 = 0.8b1.

4. Areas of rectangles before and after changing sides:

S1 = a1b1;

S2 = a2b2 = 1.2a1 * 0.8b1 = 0.96a1b1 = 0.96S1;

S2 = 0.96S1 = (1 – 0.04) S1 = S1 – 0.04S1 = S1 – S1 * 4% / 100%.

Answer. The area of the rectangle will shrink by 4 percent regardless of which side has been enlarged and which side has been shrunk.



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