# The length of the rectangle is 5 times its width. If the width of the rectangle is increased by 50%

The length of the rectangle is 5 times its width. If the width of the rectangle is increased by 50%, and the length is decreased by 4 m, then the area of the rectangle will not change. Find the dimensions of the rectangle.

1. Let the width of this rectangle be x meters, then its length is 5 * x meters, and the area is 5 * x * x = 5 * x ^ 2 square meters.
2. After 50% increase, the width of the rectangle becomes 1.5 * x meters. After decreasing by 4 meters, the length of the rectangle became (5 * x – 4) meters. After that, the area of ​​the rectangle is (5 * x – 4) * 1.5 * x square meters.
3. It is known that the area of ​​the rectangle has not changed. Then we can write the equality:
(5 * x – 4) * 1.5 * x = 5 * x ^ 2;
7.5 * x ^ 2 – 6 * x = 5 * x ^ 2;
2.5 * x ^ 2 – 6 * x = 0;
4. Because x is not equal to 0, all terms of the equation can be canceled by x. We get:
2.5 * x – 6 = 0;
x = 6 / 2.5 = 2.4;
5. We got that the width of the rectangle is 2.4 meters. Then its length is 5 * 2.4 = 12 meters.
Answer: The rectangle is 12 meters long and 2.4 meters wide.

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