If the length of the rectangle is reduced by 2 m, and the width is increased by 4 m, then its area will increase by 12 m

If the length of the rectangle is reduced by 2 m, and the width is increased by 4 m, then its area will increase by 12 m. If each side of it is reduced by 1 m, then the area of the original rectangle will decrease by 13 m. Find the sides of the given rectangle.

Let us denote the length by the letter A, the width by the letter B. We compose a system of equations according to the data of the problem and solve it:

(A – 2) x (B +4) = A x B + 12;

(A – 1) x (B – 1) = A x B – 13.

Expand the brackets and simplify. It turns out:

4 x A – 2 x B = 20;

A + B = 14.

We express A through B in the second equation and substitute in the first:

4 x (14 – B) -2 x B = 20;

56 – 4 x B – 2 x B = 20;

6 x B = 36.

Where from:

B = 6 (m).

Respectively:

A = 14 – 6;

A = 8 (m).

Answer: the length of the rectangle is 8 m, the width is 6 m.