The length of the rectangle is 12 cm longer than its width. If the length is increased by 3 cm and the width by 2 cm

The length of the rectangle is 12 cm longer than its width. If the length is increased by 3 cm and the width by 2 cm, then the area of the rectangle will increase by 80 cm2. Find the length and width of the rectangle.

1. Let the width be x centimeters.

2. Let’s calculate the length.

(x + 12) centimeters.

3. What is the area of the rectangle?

x * (x + 12) = (x² + 12x) cm².

4. Find out the new size of the sides.

a) The length is x + 12 + 3 = (x + 15) centimeters.

b) Width (x + 2) centimeters.

5. Let’s find its area.

(x + 15) * (x + 2) = x² + 2x + 15x + 30 = (x² + 17x + 30) cm²;

6. To determine the width, compose an equation.

x² + 17x + 30 – x² – 12x = 80;

5x = 50;

x = 50/5 = 10;

x = 10 centimeters.

7. The length of the rectangle is.

x + 12 = 10 + 12 = 22 centimeters.

Answer: 10 and 22 centimeters.