Question:
A rectangular plot of land measures 55 meters by 25 meters. A path of uniform width surrounds the plot. If the area of the path is equal to the area of the plot, what is the width of the path in meters?
A rectangular plot of land measures 55 meters by 25 meters. A path of uniform width surrounds the plot. If the area of the path is equal to the area of the plot, what is the width of the path in meters?
Updated On: Aug 21, 2024
- \(5\sqrt{2} - 5\)
- \(10\sqrt{2} - 5\)
- \(15\sqrt{2} - 5\)
- \(20\sqrt{2} - 5\)
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The Correct Option is A
Solution and Explanation
Let the width of the path be 'x' meters.
Length of the outer rectangle (including the path) = (55 + 2x) meters
Breadth of the outer rectangle (including the path) = (25 + 2x) meters
Area of the outer rectangle = (55 + 2x)(25 + 2x) square meters
Area of the inner rectangle (plot) = \(55 \times 25 = 1375 \) square meters
Given, Area of the path = Area of the plot
Therefore, (55 + 2x)(25 + 2x) - 1375 = 1375
Expanding and simplifying the equation, we get:
\(4x^2 + 160x - 1375 = 0\)
Solving this quadratic equation for x, we get x = \(5\sqrt{2} - 5\)
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