If one side of the rectangle is increased by 30 percent and the other is reduced by 10 percent

If one side of the rectangle is increased by 30 percent and the other is reduced by 10 percent, then the perimeter is increased by 12 cm. If the first side is reduced by 10 percent, and the other side is reduced by 20 percent, then the perimeter will decrease by 32 cm. Find the perimeter of the rectangle.

Let a and b be the sides of the given rectangle. Let’s write down its perimeter: P = 2 * (a + b). Further, according to the condition, side a will increase by 30%, and side b will decrease by 10%, then the perimeter will increase by 12 cm.We write this in the equation: P + 12 = 2 * (1.3 * a + 0.9 * b ). Further, it is known that if side a decreases by 10%, and side b decreases by 20%, then the perimeter will decrease by 32 cm.We write this in the equation: P – 32 = 2 * (0.9 * a + 0.8 * b ). So we write three equations into a system with three unknowns P, a b.

{P = 2 * (a + b); P + 12 = 2 * (1.3 * a + 0.9 * b); P – 32 = 2 * (0.9 * a + 0.8 * b)};

Substitute the first equation into the second and third:

{2 * a + 2 * b + 12 = 2 * (1.3 * a + 0.9 * b); 2 * a + 2 * b – 32 = 2 * (0.9 * a + 0.8 * b)}. we reduce by 2 both sides of the equations and reduce the common terms:

{0.1 * b + 6 = 0.3 * a; 0.1 * a – 16 = – 0.2 * b};

Let’s multiply the equations by 10:

{b = 3 * a – 60; a = -2 * b + 160};

b = 3 * (-2 * b + 160) – 60;

b = -6 * b + 420;

b = 60 cm;

a = -2 * 60 + 160 = 40 cm;

P = 2 * (40 + 60) = 200 cm.