# A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide . if the path occupies 208 m^2 , find the width of the footpath

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The Brainliest Answer!

area of footpath = 208m^2

area of remaining field = 768-208= 560m^2

let width of footpath be x

area of remaining part = l*b

=32-2x*24-2x=560

=768-48x-64x+4x^2=560

=768-112x+4x^2=560

=-112x+4x^2=560-768

=4x(-28+x)=-208

=x(-28+x)=-52

=-28x+x^2=-52

=(-14)^2-28x+x^2=-52+(-14)^2

=196-28x+x^2=-52+196

=(x-14)^2=144

=√(x-14)^2=√144

=x-14=12

=x=12+14

=x=26

Therefore,width of the footpath= 26m