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. $5\sqrt{2} - 5$
• B. $10\sqrt{2} - 5$
• C. $15\sqrt{2} - 5$
• D. $20\sqrt{2} - 5$

Answer 1

Answer: (A)

$5\sqrt{2} - 5$

Answer 2

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 = $5\sqrt{2} - 5$