# 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.