Question

The length of a room exceeds its breadth by 3 metres. If the length is increased by 3 metres and the breadth is decreased by 2 metres, the area remains the same. Find the length and breadth of the room.

Answer 1

Let the breadth of a room $$ =x $$ m
According to the question, Length of the room $$ =x+3 $$
Then, Area of room $$ =(x+3) \times(x) \mathrm{m}^{2} $$
$$ =x^{2}+3 x $$
Condition II:Area remains same, when length $$ =(x+3+3) m=(x+6) m $$
and breadth $$ =(x-2) \mathrm{m} $$
According to the question, $$ x^{2}+3 x=(x+6)(x-2) $$
$$ \Rightarrow x^{2}+3 x=x^{2}-2 x+6 x-12 $$
$$ \Rightarrow 3 x=4 x-12 $$
$$ \Rightarrow 3 x-4 x=-12 $$
$$ \Rightarrow x=12 $$
So, length of the room $$ =(x+3)=12+3=15 \mathrm{m} $$
Hence, the length of the room is $$ 15 \mathrm{m} $$ and the breadth of a room is $$ 12 \mathrm{m} $$