The width of the rectangle is 3 m less than its length. If the width of this rectangle is increased by 5 m

The width of the rectangle is 3 m less than its length. If the width of this rectangle is increased by 5 m, and the length is reduced by 2, then its area will increase by 20m². Find the area of the given rectangle.

Let’s denote the area of the declared rectangle:

S = A x B,

where A is the length and B is its width.

Let B = X, then A = X + 3.

The area of the transformed rectangle is denoted by:

S ’= A’ x B ’,

where A ‘= X + 3 – 2 = X + 1, and B’ = X + 5.

By condition:

S ’- S = 20 (m²).

Substitute expressions for S ‘and S:

(X + 1) x (X + 5) – (X + 3) x X = 20;

X² + 6 x X + 5 – X² – 3 x X = 20;

3 x X + 5 = 20;

3 x X = 15;

X = 5 (m).

Now there is nothing easier to find the area of a given rectangle:

S = 5 x (5 +3);

S = 5 x 8;

S = 40 (m²).

Answer: the area of this rectangle is 40 m².