One side of a rectangle exceeds its other side by 2 cm. If its area is 195cm ², determine the sides of the rectangle.

Let the breadth of the rectangle be x cm.
Then the length of the rectangle is (x + 2) cm.
Area of the rectangle = length × breadth = (x + 2) × x = x ² + 2x
x ² + 2x = 195
x ² + 2x – 195 = 0
x ² + 15x – 13x – 195 = 0
x(x + 15) – 13(x + 15) = 0
(x – 13)(x + 15) = 0
x = 13 or x = –15
Therefore the sides of the rectangle is 13 cm and 15 cm.
Checking :
13 cm × 15 cm = 195 cm ^2.