Question

`Length of a rectangle is 8 cm more than its breadth. If Length is decreased by 5 cm and breadth is increased by 3 cm so that area is reduced by 55 cm^{2} thenperimeter of the rectangle is`​

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.