The perimeter of the rectangle is 60 cm. If one side of it is reduced by 5
The perimeter of the rectangle is 60 cm. If one side of it is reduced by 5 cm and the other is increased by 3 cm, then its area will decrease by 21 square cm. Find the sides of the rectangle.
Let us denote the lengths of the sides of this rectangle through x and y.
Then the area of this rectangle will be x * y.
If one side of this rectangle is reduced by 5 cm, and the other is increased by 3 cm, then the area of the resulting rectangle will be (x – 5) * (y + 3).
According to the condition of the problem, as a result of this, the area of the rectangle will decrease by 21 square meters. see, therefore, we can write the following relation:
(x – 5) * (y + 3) = x * y – 21.
Simplifying this ratio, we get:
x * y + 3x – 5y – 15 = x * y – 21;
3x – 5y = 15 – 21;
3x – 5y = -6;
3x = 5y – 6;
x = (5/3) y – 2.
According to the condition of the problem, the perimeter of the rectangle is 60 cm.
Therefore, the sum of the lengths of the sides of this rectangle is 60/2 = 30 cm and we can draw up the following equation:
(5/3) y – 2 + y = 30.
We solve the resulting equation:
(5/3) y + y = 30 + 2;
(8/3) y = 32;
y = 32 / (8/3);
y = 3 * 32/8;
y = 3 * 4;
y = 12 cm.
Knowing y, we find x;
x = (5/3) y – 2 = (5/3) * 12 – 2 = 5 * 4 – 2 = 20 – 2 = 18 cm.
Answer: the sides of the rectangle are 18 cm and 12 cm.