A rectangle has an area of 100 in2 and a perimeter of 50 in

A rectangle has an area of 100 in² and a perimeter of 50 in. Find the dimensions of the rectangle.

The dimensions of the rectangle are ? in by ? in.

Solution

Let the dimensions of the rectangle be x inches by y inches. Then, xy = 100 and 2x+2y = 50 or, x +y = 25. Since y = 100/x, on substituting this value of y in the other equation, we get x+100/x = 25 or, (x²+100)/x = 25 or, x²+100 = 25x or, x² -25x+100 = 0 or, x² -20x -5x+100 = 0 or, x(x-20)-5(x-20) = 0 or, (x-20)(x-5) = 0. Thus either x = 20 or, x = 5. If x = 20, then y = 100/20 = 5 and if x = 5, then y = 100/5 = 20. Thus, the dimensions of the rectangle are 20 inches by 5 inches.