How much is the length of the rectangle greater than its width if the perimeter of the rectangle
| April 18, 2021 | education
How much is the length of the rectangle greater than its width if the perimeter of the rectangle is 32cm and the area is 55cm ^ 2.
Find half of the perimeter of the rectangle.
32 cm ÷ 2 = 16 cm.
Let’s represent one side of the rectangle as x, and the other side as 16 – x. Their product will be equal to the area of the rectangle, which is 55 cm². Let’s compose and solve the equation.
x * (16 – x) = 55.
16 * x – x² = 55
-16 * x + x² = -55.
x² – 16 * x + 55 = 0.
D = 256 – 4 * 1 * 55 = 36.
x1 = (16 – 6) ÷ 2 = 5.
x2 = (16 + 6) ÷ 2 = 11.
The width is 5 cm, the length is 11 cm. Let’s find their difference.
11 cm – 5 cm = 6 cm.
Answer: the length of the rectangle is 6 cm more than the width.
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