Question

The length and breadth of a rectangular field are 38 m and 32 m . A path of uniform width exists within the field along the boundary. If the area of the path is 600 sq.m , then find the width of the path​

Answer 1

Answer:

let the width of the path is x m

then,without path length and breadth are

(38-2x) m and (32-2x) m

so ,

38×32-(38-2x)(32-2x)=600

=> 38×32-(38×32-64x-76x+4x^2=600

=> 38×32-38×32+64x+76x-4x^2=600

=> 140x-4x^2-600=0

=> -4(x^2-35x+150)=0

=> x^2-35x+150=0

=> x^2-30x-5x+150=0

=> x(x-30)-5(x-30)=0

=> (x-30)(x-5)=0

=> x-30=0

=> x=30

x-5=0

=> x=5

x is not equal to 30 because width of the path is not 30 m as breadth is 32 m

so width of the path is 5 m