Question:
A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. The total area of the walkway is 516 m$^2$. How wide, in metres, is the walkway?
A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. The total area of the walkway is 516 m$^2$. How wide, in metres, is the walkway?
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When a uniform walkway surrounds a rectangle, enlarge both length and width by twice the walkway’s width.
Updated On: Aug 4, 2025
- 4.3 m
- 3 m
- 43 m
- 3.5 m
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The Correct Option is A
Solution and Explanation
Let width of walkway be $x$. Outer rectangle dimensions: $(20+2x)$ and $(60+2x)$. Area of walkway: $(20+2x)(60+2x) - (20)(60) = 516$. Expanding: $1200 + 40x + 120x + 4x^2 - 1200 = 516 \Rightarrow 160x + 4x^2 = 516 \Rightarrow x^2 + 40x - 129 = 0$. Solving: $x = \frac{-40 + \sqrt{1600 + 516}}{2} \approx 4.3$.
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