Question

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. 

Answer 1

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.