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Home » A rectangular filed in long and wide. There is a path of uniform width all around it, having an area of . Find the width of the path
A rectangular filed in 16 \mathrm{~m} long and 10 \mathrm{~m} wide. There is a path of uniform width all around it, having an area of 120 \mathrm{~m}^{2}. Find the width of the path
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
A rectangular filed in 16 \mathrm{~m} long and 10 \mathrm{~m} wide. There is a path of uniform width all around it, having an area of 120 \mathrm{~m}^{2}. Find the width of the path

Let the width of the path be x \mathrm{~m}.

\therefore Length of the field including the path =16+x+x=16+2 x

Breadth of the field including the path =10+x+x=10+2 x

Now,
(Area of the field including path) – (Area of the field excluding path) = Area of the path
\begin{array}{l} \Rightarrow(16+2 x)(10+2 x)-(16 \times 10)=120 \\ \Rightarrow 160+32 x+20 x+4 x^{2}-160=120 \\ \Rightarrow 4 x^{2}+52 x-120=0 \\ \Rightarrow x^{2}+13 x-30=0 \\ \Rightarrow x^{2}+(15-2) x+30=0 \\ \Rightarrow x^{2}+15 x-2 x+30=0 \\ \Rightarrow x(x+15)-2(x+15)=0 \\ \Rightarrow(x-2)(x+15)=0 \\ \Rightarrow x-2=0 \text { or } x+15=0 \\ \Rightarrow x=2 \text { or } x=-15 \\ \Rightarrow x=2(\because \text { Width cannot be negative }) \end{array}

Thus, the width of the path is 2 \mathrm{~m}.

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