Question

If the lenght of a rectangle is decreases by 2m & the breadth increases by 2m the area would increases by 8 sq.m .If the lenght is decreases by 3m & the breadth decreases by 1m . The area would decreases by 27 sq.m .
What. is the lenght & breadth?​

Answer 1

Answer:

Let length and breadth of the rectangle is x and y,

Then as per first condition ,

(x−5)(y+3)=xy−9

xy−5y+3x−15=xy−9

3x−5y=6 −−−−−(1)

As per second condition,

(x+3)(y+2)=xy+67

xy+3y+2x+6=xy+67

2x+3y=61 −−−−−(2)

On multiplying equation (1) by 3 and equation (2) by 5 then adding, we get

9x−15y=18

10x+15y=305

−−−−−−−−−−

19x=323

∴x=17

Hence, the length of the rectangle is 17m