The width of the rectangle is half its length. If you increase the width by 3 cm and the length by 2 cm

The width of the rectangle is half its length. If you increase the width by 3 cm and the length by 2 cm, then its area will increase by 78 cm ². Find the length and width of the rectangle.

Let the width of the rectangle be x (x) cm, then, according to the problem statement, the length is (x • 2) cm. After the increase, the width of the figure became (x + 3) cm, and the length – (x • 2 + 2) cm. The initial area of the rectangle : (x • 2 • x) cm², and after enlarging the sides (x + 3) • (x • 2 + 2) cm². Knowing the difference in areas, we make the equation:
(x + 3) • (x • 2 + 2) – (x • 2 • x) = 78;
x² • 2 + 6 • x + 2 • x + 6 – x² • 2 = 78;
8 • x = 78 – 6;
8 • x = 72;
x = 72: 8;
x = 9 (cm) – the width of the rectangle;
Let’s define the length: x • 2 = 9 • 2 = 18 (cm).
Answer: The width of the rectangle is 9 cm and the length is 18 cm.