if the length and breadth of a room increased by 1 metre each the area is increased by 21 square metres if length is decreased by 1 metre and breadth is increased by 2 metre area is increased by 14 square metres find the perimeter of room

Dear student,Let the length of the room is represented by'l'and breadth by'b'. We know that Area of floor =l*b.Given that length and breadth of the room is increased by 1m.New Area=>(l+1)*(b+1).Given that area of the floor is increased by 21m2.=>(l+1)*(b+1)=lb+21=>(l+1)*(b+1)-lb=21=>lb+l+b+1-lb=21=>l+b+1=21=>l+b=20  --------(1)Given that length is decreased by 1m and breadth is increased by 2m.=>length = l-1=> breadth = b+2Given that area is increased by 14m2.New area=(l-1)(b+2)=lb+14=>(l-1)(b+2)-lb=14=>lb+2l-b-2-lb=14=> 2l-b=14+2=>2l-b=16  ------(2)From equation (1) i.e., l+b=20=>b=20-l      -------(3)Now, put (b=20-l) in equation (2)=>2l-b=162l-(20-l)=162l-20+l=163l=36l=12mPut l=12 in equation (3)b=20-lb=20-12 b=8mWe need to find the perimeter of the roomPerimeter of the room = 2(l+b)2(12+8)2×20Perimeter of the room =40mRegards

  • 0
What are you looking for?