Question

If the length and the breadth of a room are
increased by 1 metre, the area is increased by
21 square metres. If the length is increased by
1 metre and breadth is decreased by 1 metre the
area is decreased by 5 square metres. Find the
perimeter of the room.
(ICSE)​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

let l = x m

let b= y m

ATQ

x+1*y+1=xy+21 eq 1

x+1*y-1=xy-5 eq 2