The perimeter of the rectangle is 48 cm. If one side of it is doubled and the other is reduced by 6 cm

The perimeter of the rectangle is 48 cm. If one side of it is doubled and the other is reduced by 6 cm, then the perimeter of the new rectangle will be 64 cm. Find the sides of this rectangle.

1. Let’s denote the sides of the rectangle by a and b. Then the perimeter will be 2 * (a + b). By condition, the perimeter is 48 cm.We get:

2 * (a + b) = 48;

a + b = 48/2;

a + b = 24.

a = 24 – b.

2. Increase side a by 2 times, and decrease side b by 6. The perimeter of this rectangle will be 2 * (2a + (b – 6)). By condition, this perimeter is 64 cm.We get:

2 * (2a + (b – 6)) = 64;

2a + (b – 6) = 64/2;

2a + b – 6 = 32;

2a + b = 32 + 6;

2a + b = 38;

3. Substitute into the equation of item 2 the value a from item 1:

2 * (24 – b) + b = 38;

48 – 2b + b = 38;

-b = 38 – 48;

-b = -10;

b = 10 cm.

4. Find side a:

a = 24 – b;

a = 24 – 10;

a = 14.

Answer: the sides of a given rectangle are 10 and 14 cm.