The rectangle has a perimeter of 12.2 and an area of 9.1. Determine the sides of the rectangle.
March 29, 2021 | education
| We denote the sides of the rectangle through a and b.
The perimeter equals:
2a + 2b = 12.2;
The area is equal to:
a * b = 9.1
In the expression a * b = 9.1, we express in through a:
b = 9.1 / a;
Substitute the expressed value into the first expression and find a:
2a + 2 * 9.1 / a = 12.2;
2a ^ 2 + 18.2 = 12.2 a;
2a ^ 2 – 12.2a + 18.2 = 0;
a ^ 2 – 6.1a + 9.1 = 0
We solve the quadratic equation:
a 1.2 = (6.1 ± √37.21 – 4 * 9.1) / 2;
a 1.2 = (6.1 ± √0.81) / 2;
a 1 = (6.1 + 0.9) / 2 = 3.5;
a 2 = (6.1 – 0.9) / 2 = 2.6;
Find the value in:
in 1 = 9.1 / a = 9.1 / 3.5 = 2.6;
in 2 = 9.1 / 2.6 = 3.5.
Answer: a 1 = 3.5, in 1 = 2.6; a 2 = 2.6, b 2 = 3.5
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