a rectangular field is 16 m long and 10 m wide. there is a path of uniform width all around it having an area of 120m square . find the width of the path

area of path= area of big rect- area of small rect

assume width of path to be x cm

so, 120m2= (16+2x)(10+2x)- (16*10)

120= (160+ 20x +32x+ 4x2)- 160

0= 4x2 + 52x- 120

= x2+13x-30

x2+15x-2x-30

x(x+15)- 2(x+15)

(x+15)(x-2)

since width can't be negative, x=2m)

ans: 2m