The length of the rectangle is 6 cm longer than its width. After the length of the rectangle was increased by 9 cm

The length of the rectangle is 6 cm longer than its width. After the length of the rectangle was increased by 9 cm and the width was increased by 12 cm, its area increased by 3 times. Find the perimeter of the original rectangle.

1.x cm – the width of the rectangle.

x + 6 cm – the length of the rectangle.

2. Let’s compose and solve the equation.

(x + 6 + 9) * (x + 12) / x * (x + 6) = 3;

(x + 15) * (x + 12) / (x ^ 2 + 6x) = 3;

x ^ 2 + 12x + 15x + 180 = 3x ^ 2 + 18x;

2x ^ 2 – 9x – 180 = 0;

x = 9 + √ (81 + 4 * 2 * 180) / 4;

x = (9 + √1521) / 4;

x = (9 + 39) / 4;

x = 48/4;

x = 12.

3. The width of the rectangle is 12 cm.

4. Determine the length of the rectangle.

12 + 6 = 18 cm.

5. Determine the perimeter of the rectangle.

2 * (12 + 18) = 60 cm.

Answer: the perimeter of the rectangle is 60 cm.