The length of the rectangle is three times its width. If the length is increased by 2 cm, and the width by 4 cm

The length of the rectangle is three times its width. If the length is increased by 2 cm, and the width by 4 cm, then its area will increase by 78 cm. Find the length and width of the rectangle.

1. Let’s say the width of the rectangle is x centimeters.

2. Then the length is x * 3 = 3 centimeters.

3. Let’s calculate its area.

x * 3x = 3x cm².

4. Let’s define the sides after enlargement.

a) The width is (x + 4) centimeters.

b) Length (3x + 2) centimeters.

5. We recognize the area.

(x + 4) * (3x + 2) = 3x² + 2x + 12x + 8 = 3x² + 14x + 8;

6. Make an equation and find the width.

3x² + 14x + 8 – 3x² = 78;

14x = 70;

x = 70/14 = 5 centimeters.

7. The length is x * 3 = 5 * 3 = 15 centimeters.

Answer: 5 and 15 centimeters.