Question

# Length and breadth of rectangle ABCD are l cm and b cm respectively. If width of green coloured path is w cm, then which of the following represents brown coloured area(l+b−w)wlb−(l+b−w)wlb+(l+b−w)wlb−(l+b+w)w

Solution

## The correct option is B lb−(l+b−w)wGiven : AB=CD = l cm, BC=AD = b cm.      EF=IJ=LK=GH=MN=OP=MP=ON= w cm. Area of rectangle ABCD        = length×breadth = l×b = lb cm2 Area of rectangle EFJI       = breadth×width = b×w = bw cm2 Area of rectangle LGHK       = length×width = l×w = lw cm2 Area of square MNOP      = side2 = MN2 = w2 cm2 Brown coloured area  = Area of rectangle ABCD - Area of green colored path = Area of rectangle ABCD  - (Area of rectangle EFJI + Area of rectangle LGHK - Area of square MNOP) =  lb−(bw+lw−w2) =  lb−(l+b−w)w

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