$A s q u a r e l a w n h a s a p a t h o f 4 m a r o u n d i t . T h e a r e a o f t h e p a t h i s 196 m^{2} . F i n d t h e s i d e l e n g t h o f t h e l a w n .$

8 m

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8.15 m

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8.25 m

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8.5 m

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Solution

The correct option is C
8.25 m

$L e t t h e s i d e o f t h e l a w n = x S o, A r e a o f l a w n = x^{2} A r e a o f (l a w n + p a t h) = (x + 8)^{2} A c c o r d i n g t o q u e s t i o n, (x + 8)^{2} - (x)^{2} = 196 \Rightarrow x^{2} + 16 x + 64 - x^{2} = 196 \Rightarrow 16 x = 196 - 64 \Rightarrow 16 x = 132 \Rightarrow x = 8.25 S o, s i d e l e n g t h o f t h e l a w n = 8.25 m .$

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A square lawn has a path of 4m around it . The area of the path is 196m2. Find the side length of the lawn.

The correct option is C 8.25 m Let the side of the lawn=xSo, Area of lawn=x2Area of (lawn + path)=(x+8)2According to question,(x+8)2−(x)2=196⇒ x2+16x+64−x2=196⇒ 16x=196−64⇒ 16x=132⇒x=8.25So, side length of the lawn=8.25m.

$A s q u a r e l a w n h a s a p a t h o f 4 m a r o u n d i t . T h e a r e a o f t h e p a t h i s 196 m^{2} . F i n d t h e s i d e l e n g t h o f t h e l a w n .$