Question

The area of a rectangle increases by 200 sq m, if the length is increased by 8 m and breadth by 3 m. The area increases by 255 sq m, If the length is increased by 3m and breadth by 8 m, find the length and breadth of the rectangle.

Answer 1

We know that the area of rectangle is of the form xy where length=x and breadth=y

Now according to QUESTION,

(x+8)(y+3)=xy+200
xy+3x+8y+24=xy+200
3x+8y=176---------(i)

It is also given that
(x+3)(y+8)=xy+255
xy+8x+3y+24=xy+255
8x+3y=231---------(ii)


\To solve the 2 equations we have to make coeefficeints of x or y the same
So 8(i)-3(ii)
8(i)=>24x+64y=1408
3(ii)=>24x+9y=693

8(i)-3(ii)=>55y=715
y=715/55=13

Therefore breadth is 13

Substitute y in i
3x+8(13)=176
x=(176-104)/3=24

Therefore length =24
Breadth=13




=176