The length of the rectangle is 3 times its width, if the length is increased by 2m and the width by 3m

The length of the rectangle is 3 times its width, if the length is increased by 2m and the width by 3m, its area will increase by 72m, find the length and width of the rectangle.

1. S – area.

2. We take the width of the rectangle as x, its length -3x.

3. S = 3x².

4. S (after changing the parameters of the rectangle) = (x + 3) x (3x + 2) = 3x² + 2x + 9x + 6 = 3x² + 11x + 6.

5. Considering that the area of the rectangle after changing its parameters is larger

the initial area of 72 m², we make the equation:

3x² + 11x + 6 – 3x² = 72;

11x = 66;

x = 6.

The width of the rectangle is 6 m.

Length 6 x 3 = 18 m.

Answer: the width of the rectangle before changing its parameters is 6 m, the length is 18 m.