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

March 31, 2021 | education

| **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.

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