The perimeter of the rectangle is 60 cm. If the length of the rectangle is increased by 10 cm and the width is reduced

The perimeter of the rectangle is 60 cm. If the length of the rectangle is increased by 10 cm and the width is reduced by 6 cm, then the area of the rectangle will decrease by 32 cm square. Find the area of the rectangle.

1. Let x – the length of the rectangle, y – the width;
2. Let’s express the perimeter:
2 * (x + y) = 60;
y = 30 – x;
3. Changed length:
x + 10;
4. Reduced width:
y – 6 = 30 – x – 6 = 24 – x;
5. Initial area of the rectangle:
x * y;
6. Changed area:
(x + 10) * (y – 6);
7. Let’s compose the equation:
x * y = (x + 10) * (y – 6) + 32;
x * y = x * y – 6x + 10y – 60 + 32;
10y – 6x = 28;
10 * (30 – x) – 6x = 28;
300 – 10x – 6x = 28;
16x = 272;
x = 17;
y = 13;
8.S = x * y = 17 * 13 = 221 cm2;
Answer: 221 cm2.