The length of the rectangle is 5 cm longer than its width. If the length of the rectangle is increased by 4 cm and the width

The length of the rectangle is 5 cm longer than its width. If the length of the rectangle is increased by 4 cm and the width by 2 cm, then the area will increase by 42 cm2. find the length and width of the given rectangle.

Let’s denote the width of the rectangle through x, then the length will be (x + 5).

The area of a rectangle is equal to the product of two dimensions, length by width, that is, S = x (x + 5).

Following the condition, after changing the values, we get the following equation:

(x + 2) (4 + x + 5)) = x * (x + 5) + 42.

Let’s expand the brackets and simplify the expression: (x + 2) (9 + x) = x ^ 2 + 5x + 42 →

9x + x ^ 2 + 18 + 2x = x ^ 2 + 5x + 42.

We transfer the terms with x to one side, and the numerical ones to the other side of the equality:

9x + 2x – 5x = 42 – 18 → 6x = 24 → x = 4.

Answer: Width – 4 cm. Length – 9 cm.