Question

If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq.m. If the length is increased by 1 m and breadth is decreased by 1 m, then the area is decreased by 5 sq.m. The perimeter of the floor is:

• A. 30 m
• B. 32 m
• C. 36 m
• D. 40 m
• E. 45 m

Answer 1

The correct option is D

40 m

Let length = `x' metres and breadth = `y' metres. Then, (x+1)(y+1) -- xy = 21 $\Rightarrow$ x + y = 20 And, xy -- [(x+1) (y-1)] = 5 $\iff$ x -- y = 4 Solving (i) and (ii), we get: x = 12 and y = 8 So, length = 12 m and breadth = 8 m $\therefore$Perimeter = [2(12 + 8)] m = 40 m