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------------------------------------------------ A rectangular plot measures 12 m by 5 m. A path of constant width runs along one side and one end. If the total area of the plot and the path is 120 m², find the width of the path.

Question

College

Answer :

morningWave14 morningWave14 · Answer 1 · 2025-02-08T13:50:13-05:00

The width of the part is 3 meters.

Let's assume the width of the part is x meters.

The area of the rectangular plot is given by length multiplied by width, which is 12 m x 5 m = 60 m².

The total area of the plot and the part is given as 120 m². So, the area of the part is 120 m² - 60 m² = 60 m².

The area of the part is equal to the length of the part multiplied by its width, which is 60 m² = (12 + x) m * x m.

Simplifying the equation: 60 = 12x + x².

By rearranging the equation and solving for x, we get x² + 12x - 60 = 0.

Using the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a, we can find the value of x.

By solving the quadratic equation, we find two possible solutions: x = 3 or x = -15.

Since the width cannot be negative, the width of the part is 3 meters.

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