A rectangular pool $20$ metres wide and $60$ metres long is surrounded by a walkway of uniform width. If the total area of the walkway is $516$ square metres, how wide in metres, is the walkway?

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Solution

Let the width of the walkway be $x m$
Length becomes $(60 + 2 x)$ and Breadth becomes $(20 + 2 x) .$

Area of rectangular pool $= 20 \times 60 = 1200 m^{2}$

Area of complete rectangular pool with walkway= $(20 + 2 x) \times (60 + 2 x) = (1200 + 160 x + 4 x^{2}) m^{2}$

Area of walkway $= 516$
$(1200 + 160 x + 4 x^{2}) - 1200 = 516 \to 4 x^{2} + 160 x = 516 \to x^{2} + 40 x - 129 = 0 \to x^{2} + 43 x - 3 x - 129 = 0 \to (x + 43) (x - 3) = 0 \to x = 3$

So The width of walkway is $3 m$

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A rectangular pool 20 metres wide and 60 metres long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square metres, how wide in metres, is the walkway?

A rectangular pool $20$ metres wide and $60$ metres long is surrounded by a walkway of uniform width. If the total area of the walkway is $516$ square metres, how wide in metres, is the walkway?