The area of the rectangle is 120 cm2. Its length is 7 cm longer than its width. Find the perimeter of the rectangle.

Let the width of the rectangle be x (x) cm, then its length is (x + 7) cm.Using the formula for finding the area of ​​the rectangle, we compose and solve the quadratic equation:

x (x + 7) = 120;

x² + x · 7 – 120 = 0;

D = 7² – 4 (- 120) = 49 + 480 = 529.

x (1) = (- 7 + √529): 2 = (- 7 + 23): 2 = 8 (cm).

x (2) = (- 7 – √529): 2 = (- 7 – 23): 2 = – 15. This root of the equation does not satisfy the condition of the problem, since the size of the side of the rectangle cannot be expressed as a negative number. Therefore, the width of the figure is 8 cm.

Find the length of the rectangle: x + 7 = 8 + 7 = 15 (cm).

Using the formula, we calculate the perimeter of the rectangle: P = (a + b) 2 = (8 + 15) 2 = 46 cm.