# One side of the rectangle is 20 cm larger from the other. If the large side is reduced by 3 times

One side of the rectangle is 20 cm larger from the other. If the large side is reduced by 3 times, and the smaller side is increased by 2 times, then the perimeter of the rectangle will be 200 cm. Find the sides of the given rectangle.

Let’s designate the width as x cm, then the length is (x + 20) cm.If the length is reduced by 3 times, and the width is increased by 2 times, then the perimeter will be 200 cm. Let’s make the equation:

P = 200;

2 * (a + b) = 200;

2 * ((x + 20) / 3 + 2 * x) = 200;

(x + 20) / 3 + 2 * x = 100;

(x + 20 + 2 * x * 3) / 3 = 100;

(7 * x + 20) / 3 = 100;

7 * x + 20 = 300;

7 * x = 280;

x = 40 cm.

Find the width of the rectangle: x = 40 cm.

The length of the quadrangle: x + 20 = 40 + 20 = 60 cm.

Answer: 40 cm, 60 cm.

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