the area of a room 28 sq.m . if the length of the room was 1 m less and its breadth was 2m more than it would be in the shape of a square find the length and breadth of the room
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The length and breadth of the room are 7m and 4m respectively.
Let the length of the room be l m and breadth be b m.
If it is a rectangle, then the area of the rectangle would be lb m².
lb = 28 ...(1)
New length = (l-1) m
New breadth = (b+2) m
It is a square. So, length = Breadth
l-1 = b+2
⇒l = b+3
Replacing this value of l in (1), we get
b(b+3) = 28
⇒ b² + 3b - 28 = 0
⇒ b² +7b - 4b - 28 = 0
⇒ b(b+7) -4(b+7) = 0
⇒ (b+7)(b-4) = 0
According to zero product rule, we get
b = -7 which is not possible as breadth cannot be negative.
b = 4 m
So, l = 28/b = 28/4 = 7m
Length = 7m and Breadth = 4m
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