The width of the rectangle was increased by 3.6 cm and the length was reduced by 16%.

| August 16, 2021 | education

The width of the rectangle was increased by 3.6 cm and the length was reduced by 16%. The area of the new rectangle turned out to be 5% more than the area of the previous one. Find the width of the new rectangle.

Let the width of the original rectangle be X cm and the length equal to Y cm.

Then the width of the new rectangle is (X + 3.6) cm, and the length of the new rectangle is (Y – 0.16 * Y) = 0.84 * Y cm.

The area of ​​the original rectangle is: S1 = X * Y.

The area of ​​the new rectangle is: S2 = (X + 3.6) * 0.84 * Y.

By condition, S2 = S1 + 0.05 * S2 = 1.05 * S1.

Then 1.05 * S1 = (X + 3.6) * 0.84 * Y.

S1 = ((X + 3.6) * 0.84 * Y) / 1.05.

X * Y = ((X + 3.6) * 0.84 * Y) / 1.05.

X * Y * 1.05 = ((X + 3.6) * 0.84 * Y).

1.05 * X = 0.84 * X + 3.024.

0.21 * X = 3.024.

X = 3.024 / 0.21 = 14.4 cm.

Then the width of the new rectangle is (14.4 + 3.6) = 18 cm.

Answer: The width of the new rectangle is 18 cm.



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