The perimeter of the rectangle is 62cm and its area is 238cm². Find the sides of the rectangle.

Let’s denote the sides of the rectangle as a and b.
The perimeter of the rectangle is:
2 a + 2 b = 62 cm;
a + b = 31 cm.
The area of the rectangle is:
a b = 238 cm2.
Let’s make a quadratic equation:
a b = a (31 – a) = 238;
a ^ 2 – 31 a + 238 = 0;
a = (31 ± √ (31 ^ 2 – 4 * 238)) / 2 = (31 ± 3) / 2;
a1 = 17;
a2 = 14.
b1 = 31 – a1 = 14.
b2 = 31 – a2 = 17.
Thus, a rectangle with sides 17cm, 14cm.