The perimeter of the rectangle is 42 and the area is 108. Find the larger side of the rectangle.

Rectangle area:

S = a * b = 108.

Perimeter of the rectangle:

P = 2a + 2b = 42;

a + b = 42/2 = 21.

We have a system of equations:

1) a * b = 108,

2) a + b = 21.

From the second equation, we express a through b and substitute the resulting value into the first equation:

a = 21 – b;

(21 – b) * b = 108;

b ^ 2 – 21b + 108 = 0.

Having solved the resulting quadratic equation, we find the sides of the rectangle:

D = 21 ^ 2 – 4 * 108 = 441 – 432 = 9 = 3 ^ 2;

b1 = (21 – 3) / 2 = 18/2 = 9;

b2 = (21 + 3) / 2 = 24/2 = 12.

The large side of this rectangle is 12.