A square lawn is surrounded by a path $2.5 m$ wide. If the area of the path is $165 m^{2} .$ Find the area of the lawn.

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Solution

$\begin{matrix} L e t t h e s i d e o f t h e l a w n b e x w i d t h o f t h e p a t h = 2.5 m s i d e o f t h e l a w n i n c l u d i n g p a t h = x + 2 (2.5 m) = x + 5 m S o, a r e a o f l a w n = a r e a o f t h e l a w n i n c l u d i n g t h e p a t h - a r e a o f t h e p a t h A r e a o f a s q u a r e = {(s i d e)}^{2} N o w, x^{2} = {(x + 5)}^{2} - 165 x^{2} = (x^{2} + 10 x + 25) - 165 x^{2} = x^{2} + 10 x + 25 - 165 x^{2} - x^{2} + 10 x = 140 10 x = 140 ∴ x = 14 S i n c e, t h e s i d e o f t h e l a w n = 14 m H e n c e, t h e a r e a o f t h e l a w n = {(14)}^{2} o r 196 m^{2} . \end{matrix}$

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A square lawn is surrounded by a path 2.5m wide. If the area of the path is 165m2. Find the area of the lawn.

A square lawn is surrounded by a path $2.5 m$ wide. If the area of the path is $165 m^{2} .$ Find the area of the lawn.