One side of the rectangle is 5 cm larger than the other, and its area is 84 cm. Find the sides of the rectangle.

In order to find the sides of a rectangle, knowing that one side of the rectangle is 5 cm larger than the other, and the area of the rectangle is 84 cm2.

Let’s denote one of the sides of the rectangle with the variable x cm, then the second side is (x + 5) cm.

Let’s remember and apply the formula for finding the area of a rectangle.

S = a * b;

x (x + 5) = 84;

x ^ 2 + 5x – 84 = 0;

D = b ^ 2 – 4ac = 25 – 4 * 1 * (-84) = 25 + 336 = 361;

x1 = (-b + √D) / a = (-5 + √361) / 2 = (-5 + 19) / 2 = 14/2 = 7;

x2 = (-b – √D) / a = (-5 – √361) / 2 = (-5 – 19) / 2 = -24/2 = -12;

So, one side of the rectangle is 7 cm, then the second side is 7 + 5 = 12 cm.