if the length and breadth of a room increased by 1 metre each the area is increased by 21 square - Maths - Simultaneous Linear Equations

Question

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

Komal Garg · Accepted Answer

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=16⇒2l-(20-l)=16⇒2l-20+l=16⇒3l=36⇒l=12mPut l=12 in equation (3)⇒b=20-l⇒b=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

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