Question: The length of a room is 2m longer than its breadth. If the area of the room is 63sq.m. find the length and breadth of the room.

Solution:

Let the length of the room be l m and the breadth of that room be b m.

According to the question,

Condition I,
Length is 2m longer than the breadth.
or, l = b+2 - (i)

Condition II,
Area of the room is 63 m².
or, lb = 63
[Put value of l from equation (i) ]
or, (b+2)b = 63
or, b² + 2b -63 = 0
or, b² + (9-7)b -63 = 0
or, b² +9b -7b -63 = 0
or, b(b +9) -7(b +9) = 0
or, (b -7)(b +9) = 0

Either,
b -7 = 0
\therefore b = 7

Or,
b +9 = 0
\therefore b = -9

Since, distance can never be negative, out value of b = 7 in equation (i), we get,

or, l = 7+2
\therefore l = 9

So, (l,b) = (9,7)

Therefore, the required length and breadth of the room are 9m and 7m respectively.

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