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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