The perimeter of the rectangle is 20cm. Find its sides if you know that the area of the rectangle is 24cm.
September 21, 2021 | education
| 1. The formula for the perimeter of a rectangle is P = 2 * (a + b). Let us express b in terms of a:
20 = 2 * (a + b);
a + b = 10;
b = 10 – a.
2. The area formula for a rectangle S = a * b. Substitute the values and solve the resulting equation:
24 = a * (10 – a);
10a – a2 – 24 = 0;
a2 -10a + 24 = 0;
D = 100 – 96 = 4;
a1 = (10 + 2) / 2 = 6;
a2 = (10 – 2) / 2 = 4;
b1 = 10 – 6 = 4;
b2 = 10 – 4 = 6.
Answer: the sides of the rectangle are 6 cm and 4 cm.
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