The perimeter of the rectangle is 44 cm and its area is 105 cm². Find the sides of the rectangle.
| March 9, 2021 | education
The perimeter of a rectangle is twice the sum of its sides.
P = 2 * (a + b).
The area of a rectangle is the product of the sides of the rectangle.
S = a * b.
If we substitute known values into these formulas, we get:
44 = 2 * (a + b).
a + b = 22 cm.
105 = a * b.
Let us express the value of the side a through the first equation.
a = 22 – c.
Substitute in the second equation:
105 = (22 – in) * in.
105 = 22 * in – in ^ 2.
b ^ 2 – 22 * b + 105 = 0.
D = 22 * 22 – 4 * 1 * 105 = 484 – 420 = 64.
L = 8 cm.
x = 22 – 8/2 = 7 cm (first side).
22 – 7 = 15 cm (second side).
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