The length of the rectangle is twice its width; if the width is increased by 3 cm and the length by 2 cm

The length of the rectangle is twice its width; if the width is increased by 3 cm and the length by 2 cm, then its area will increase by 78 cm2. Find the length and width of the rectangle.

Let the width of the rectangle be x cm, then the length of the rectangle is 2x cm. Let’s write down what is its area:
S1 = a1 * b1 = 2x * x = 2x².
After the changes, its parameters became:
(x + 3) – width;
(2x + 2) – length.
We find the area with the changed data:
S2 = a2 * b2 = (2x + 2) * (x + 3) = 2x² + 6x + 2x + 6 = 2x² + 8x + 6.
According to the condition, it is said that this area is 78 cm² larger, we draw up the equation:
2x² + 8x + 6 – 2x² = 78
8x = 72
x = 9 (cm) – the width of the rectangle;
9 * 2 = 18 (cm) – the length of the rectangle.
Answer: 18 cm and 9 cm are the length and width of the rectangle, respectively.