Find the perimeter of a rectangle that is 8 cm longer than wide and has an area of 209 cm2.
| February 11, 2021 | education
Imagine the width of the rectangle as x, then the length will be x + 8 cm. And their product will be equal to the area, which is 209 cm². Let’s compose and solve the equation.
x * (x + 8) = 209.
x² + 8 * x = 209.
x² + 8 * x – 209 = 0.
D = 8² – 4 * (-209) = 900.
x1 = (-8 + √900) ÷ 2 = 11.
x2 = (-8 – √900) ÷ 2 = -19.
The width is 11 cm and the length is 19 cm, so we find the perimeter of the rectangle.
P = (11 cm + 19 cm) * 2 = 60 cm.
Answer: the perimeter is 60 cm.
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