Question

10. If the length is increased by 2m and breadth is increased by 3m, then the area of rectangular
floor of Rafique is increased by 75 sq.m. But if the length is reduced by 2m and breadth is
increased by 3m, the area is increased by 15 sq.m. By forming simultaneous linear equations,
let us determine the length and breadth of the floor.​

Answer 1

Step-by-step explanation:

Let the length and breadth of the rectangle be X and Y. Length is increased

by 2m and Breadth is increased by 3m then Area of the rectangle =>(X+2) (Y+3)=>XY+3X+2Y+6. So increase in Area =>XY+3X+2Y+6-(XY) =>2Y+3X+6= 75 => 2Y+3X=69..(1) But if Length is reduced by 2m and Breadth is increased by 3m there is decrease in area by 57 sq.m. Add both equations (1) and (2) =>6X=12 =>X=2 and 3(2)-2Y= -57 =>2Y=63 =>Y=

=>(X-2)(Y+3) -XY= -57 =>XY+3X-2Y-6-(XY) = -57 =>3X-2Y-6= -57 =>3X-2Y= -57...(2)

31.5. Hence the length and breadth of the rectangle are 2m and 31.5m respectively. Hope it helps you.