Find the sides of the rectangle if its area is 60cm ^ 2 and the perimeter is 38cm.

A rectangle is a rectangle with right angles in which opposite sides are equal.

The area of ​​a rectangle is the product of two adjacent sides:

S = a b.

Perimeter is the sum of the lengths of its sides:

P = AB + BC + CD + AD.

Since the area of ​​the rectangle is 60 cm2, and the perimeter is 38 cm, we express this with the equation:

x is the length of the side AB and CD;

y is the length of the side BC and AD;

x y = 60;

2x + 2y = 38;

y = 60 / x;

2x + 2 60 / x = 38;

2x + 120 / x = 38;

2×2 + 120 = 38x;

2×2 + 120 – 38x = 0;

2×2 – 38x + 120 = 0;

D = b2 – 4ac;

D = 382 – 4 · 2 · 120 = 1444 – 960 = 484 = 222;

x = (-b + √D) / 2a;

x = (- (- 38) + 22) / 2 2 = 60/4 = 15;

y = 60/15 = 4;

AB = CD = 15 cm;

BC = AD = 4 cm.

Answer: the sides of the rectangle are 15 cm and 4 cm.