Question

A foothpath of uniform width runs all around the outside of a rectangular field of 30 M long and 24 M wide . If the path occupies an area of 360 square metre square,find its width.

Answer 1

let the width be x
(24)2x + (30)2x + 4x^2 =360
48x + 60x + 4x^2=360
x^2+27x-90=0
x^2+30x-3x-90=0
(x+30)(x-3)=0
x=3m=width

Answer 2

Step-by-step explanation:

Let the width of the path be x.

∴ length of the rectangular field and path =2x+30

and breadth =2x+24

Area of rectangular field =(30×24)

=720

Area of the rectangular field and path =(2x+30)(2x+24)

Now,

(2x+30)(2x+24)−720=360

⇒4x

2

+48x+60x+720−720=360

⇒4x

2

+108x−360=0

⇒x

2

+27x−90=0

⇒x

2

+30x−3x−90=0

⇒x(x+30)−3(x+30)=0

⇒(x+30)(x−3)=0

⇒x=−30 and x=3

Negative value is not valid,

∴ Width is 3 cm

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