# 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.