Question

The length of a rectangle exceeds the breadth by 6cm .if the length is increased by 3cm and breadth is decreased by 2 cm, the area remains the same .find the length and breadth of the rectangle .

Answer 1

let,

breadth = x cm
length = ( x + 6 ) cm

Area =length × breadth

Area = x(x + 6)

Area =  x² + 6x
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if length is increased by 3 and breadth is decreased by 2 

length = x + 6 + 3 = (x + 9) cm
breadth = ( x  - 2 ) cm

Area = length × breadth  
        = (x - 2) (x + 9) 
        = x² + 9x - 2x - 18
        = x²  + 7x - 18



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Given that Area remains same, 


x² + 6x = x² + 7x - 18

x² - x² + 6x - 7x = -18 

-x = - 18 

x =18 

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Then, 

breadth = x =18  cm
length = x + 6 = 18 + 6 = 24 cm



i hope this will help you


(-:

Answer 2

let the breadth of the rectangle be x cms.
therefore length=x+6 cms.
According to first condition
length is increased by 3
length=x+6+3=x+9cms
breadth is decreased by 2
breadth=x-2
According to second condition
areas of both rectangle are same
therefore
x.x+6=x-2.x+9
x square+6x=x square+9x-2x-18
x square-x square+6x=7x-18
7x-6x=18
x=18cms.
therefore breadth=18cms
length=x+6=18+6=24 cms
Length=24cms and Breadth=18cms