Question

The length of a rectangular plot of land exceeds its breadth by 23m . If the length is decreased by 15m and the breadth is increased by 7m the area is reduced by 360m ^2 find the length and breadth of the plot

Answer 1

Answer:

$\huge{\underline{\underline{\mathfrak\red{Answer\::}}}}$

$\bold\red{Length=75\:m}$

$\bold\purple{Breadth=52\:m}$

$\bold\green{Solution\::}$

Let the breadth be X m

So, length = ( X + 23) m

Area = Length × Breadth

=> Area = {(X+23)* X} m^2

=> Area = (X^2 + 23X) m^2

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Secondly:-

Length= (X +23 - 15) m = (X + 8) m

Breadth = (X + 7) m

Area = {(X + 8) * (X + 7)} m^2

=> Area = (X^2 + 15X + 56) m^2.

According to question:-

X^2 + 15X + 56 = X^2 + 23X - 360

=>X^2 + 15X - X^2 - 23X =-360 -56

=> -8X = - 416 m

=> X = -416/-8 m

=> X = 52 m

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D i m e n s i o n s : -

Breadth = X = 52 m

Length = (X+23) = (52 + 23) m = 75 m

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