Question

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

Answer 1

Let the length of the room is represented by 'l' and breadth by 'b'.

Given that length and breadth of the room is increased by 1m.

= > (l + 1) * (b + 1).  

We know that Area of floor = l * b.

Given that area of the floor is increased by 21 m^2.

= > (l + 1) * (b + 1) = lb + 21

= > (l + 1) * (b + 1) - lb = 21

= > lb + l + b + 1 - lb = 21

= > l + b + 1 = 21

= > l + b = 20    -------- (1)

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Given that length is increased by 1m and breadth is decreased by 1m.

= > length  = l + 1

= > breadth = b + 1.

Given that area is decreased by 5m.

= > (l + 1) * (b - 1) = lb - 5

= > (l + 1) * (b - 1) - lb = -5

= > lb - l + b - 1 - lb = -5

= > -(l - b)  = -4

= > l - b  = 4     ------- (2)

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On solving (1) & (2), we get

= > l + b = 20

= > l - b = 4

    ---------------

     2b = 24

       b = 12.

Substitute b = 12 in (1), we get

= > l + b = 20

= > l + 12 = 20

= > l = 8.

Now,

We know that perimeter of the floor = 2(l + b)

= > 2(8 + 12)

= > 2(20)

= > 40m.

Hope this helps!

Answer 2

☺ here is your answer OK ☺☺☺☺





Let the length and breadth of a room be x & y
Area of the room = x * y
When the length and breadth of a room are increased by 1 metre, then the new dimensions of the room would be
Length : x+1
Width : y+1
New area = (x+1)(y+1)
Since the area is increased by 21 metres, therefore
(x+1)(y+1)- xy = 21...........(1)
Further when the length is increased by 1 metre, then the area would be (x+1) * y
Now when the length is increased by 1 metre , the area is dcreased by 5 square metres
(x+1) * y -xy = 21-5............(2)
Simplifying & solving eqns 1 & 2 results in
x=4 and y=16
Perimeter of the room = 2*(Length+width)
= 2*(4+16)
Ans : 40 meter

I hope I help you ☺☺