Question

The length of a room exceeds its breadth by 3 meters .if the length is increased by 3 meters and the breadth is decreased by 2 meters the area remains the same . find the length and the breadth.

Answer 1

Suppose length and breadth of a room are l and b respectively.

so area of rectangle is = l*b = lb
length of room exceeds breath by 3 m
So; l = b+3 ...........equation <i>

breadth decreased by 2m
So; b+2

area = l*b
=> lb = {l+3} {b+2}
=> lb = lb-2l+3b-6
=> 3b-2l = 6
=> 3b-2{b+3} = 6........[using i]
=> 3b-2b-6 = 6
=> b = 12

then from i we get;
l=12+3=15

l = 15m and b = 12m 

Answer 2

Let the length of the room be x meters and the breadth of the room be y meters. 

Then, we have: 

Area of the room = xy 

According to the question, we have: 

x = y + 3

⇒ x – y = 3 …….(i) 

And, (x + 3) (y – 2) = xy 

⇒ xy – 2x + 3y – 6 = xy 

⇒ 3y – 2x = 6 ……..(ii) 

On multiplying (i) by 2, we get: 

2x – 2y = 6 ……….(iii) 

On adding (ii) and (iii), we get: 

y = (6 + 6) = 12 

On substituting y = 12 in (i), we get:  x – 12 = 3 

⇒ x = (3 + 12) = 15 

Hence, the length of the room is 15 meters and its breadth is 12 meters.