The length of the rectangle is 7 m less than its width, if the length is increased by 5 m

The length of the rectangle is 7 m less than its width, if the length is increased by 5 m and the width by 3 m, then the area will increase by 54 m.Find the length and width of the rectangle

Let the width of the figure in question be x m, then its length is (x – 7) m, and its area, respectively, is x (x – 7) m2.

In the modified figure, the length will be (x – 7 + 5) = (x – 2) m, width (x + 3) m, and the area x (x – 7) + 54 m2.

Let’s compose and solve the equation:

(x – 2) (x + 3) = x (x – 7) + 54; open brackets, make possible simplifications:

x2 + 3x – 2x – 6 = x2 – 7x + 54; we perform calculations relative to x:

8x = 60;

x = 60/8 = 7 4/8 = 7.5 m – width;

x – 7 = 7.5 – 7 = 0.5 m – length.