Question

.A path of uniform width runs around and outside a square plot of side 25 m. If the area of the path is 216 m2 then its width is (0) 2 m (2) 4 m (3) 3 m (4) 8 m ​​

Answer 1

Answer:

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

⇒4x2+48x+60x+720−720=360

⇒4x2+108x−360=0

⇒x2+27x−90=0

⇒x2+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

Explanation:

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