Question

Three times the width of a room exceeds the length by 5m if the length and breadth each are increased by 1 m then the area is increased by 12 m find the dimensions of the room

Answer 1

Let length of the room be x metres
and width be y metres
Original area of the room=xy metre^2
According to the question,
$3y = x + 5 \\ 3y - 5 = x$
But
$(x + 1)(y + 1) = xy + 12 \\ xy + x + y + 1 = xy + 12 \\ x + y - 11 = 0$
Now substitute the value of x
Therefore,
$3y - 5 + y - 11 = 0 \\ 4y = 16 \\ y = 4 \\ x = 7$

Length is 7 metres and Width is 4 metres