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प्रश्न
A rectangular filed in 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 2 120m . Find the width of the path.
उत्तर
Let the width of the path be x m.
∴Length of the field including the path =`16+x+x=16+2x`
Breadth of the field including the path=`10+x+x=10+2x`
Now,
(Area of the field including path) - (Area of the field excluding path) =
Area of the path
⇒`(16+2x)(10+2x)-(16xx10)=120`
⇒`160+32x+20x+4x^2-160=120`
⇒`4x^2+52x-120=0`
⇒`x^2+13x-30=0`
⇒`x^2+(15-2)x+30=0`
⇒`x^2+15x-2x+30=0`
⇒`x(x+15)-2(x+15)=0`
⇒`(x-2)(x+15)=0`
⇒`x-2=0 or x+15=0`
⇒`x=2 or x=-15`
⇒`x=2 ` ( ∵Width cannot be negative)
Thus, the width of the path is 2 m.
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