Question

The area of rectangle reduces by 20 if it's length is increased by 1 and the breadth is reduced by 2. The area increases by 12 , if the length is reduced by 3 and breadth is increased by4 .aFind the dimensions

Answer 1

AnswEr :

$\bf{\Large{\underline{\sf{Given\::}}}}$

The area of rectangle reduces by 20, if it's length is increased by 1 and the breadth is reduced by 2. The area increases by 12 if the length is reduced by 3 and breadth is increased by 4.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The dimensions of the rectangle.

$\bf{\Large{\underline{\rm{\orange{Explanation\::}}}}}$

Let length of rectangle be R

Let breadth of rectnagle be M

Area of rectangle = RM

$\bf{\large{\underline{\tt{\red{A.T.Q\::}}}}}$

$\hookrightarrow\tt{(R+1)(M-2)=RM-20}\\\\\\\hookrightarrow\tt{\cancel{RM}-2R+M-2=\cancel{RM}-20}\\\\\\\hookrightarrow\tt{-2R+M-2=-20}\\\\\\\hookrightarrow\tt{-2R+M=-20+2}\\\\\\\hookrightarrow\tt{\pink{-2R+M=-18.......................................(1)}}$

Again,

$\hookrightarrow\tt{(R-3)(M+4)=RM+12}\\\\\\\hookrightarrow\tt{\cancel{RM}+4R-3M-12=\cancel{RM}+12}\\\\\\\hookrightarrow\tt{4R-3M-12=12}\\\\\\\hookrightarrow\tt{4R-3M=12+12}\\\\\\\hookrightarrow\tt{\pink{4R-3M=24....................................(2)}}$

$\bf{\large{\underline{\tt{\purple{Substitution\:\:Method\::}}}}}$

From equation (1), we get;

$\leadsto\tt{-2R+M=-18}\\\\\leadsto\tt{\red{M=-18+2R.....................................(3)}}$

Putting the value of M in equation (2), we get;

$\mapsto\tt{4R-3(-18+2R)=24}\\\\\\\mapsto\tt{4R-(-54+6R)=24}\\\\\\\mapsto\tt{4R+54-6R=24}\\\\\\\mapsto\tt{-2R+54=24}\\\\\\\mapsto\tt{-2R=24-54}\\\\\\\mapsto\tt{-2R=-30}\\\\\\\mapsto\tt{R\:=\:\cancel{\dfrac{-30}{-2} }}\\\\\\\mapsto\tt{\purple{R\:=\:15\:unit}}$

Putting the value of R in equation (3), we get;

$\mapsto\tt{M\:=\:-18+2(15)}\\\\\\\mapsto\tt{M\:=\:-18+30}\\\\\\\mapsto\tt{\purple{M\:=\:12\:unit}}$

Thus,

$\bullet\sf{Length\: of\: rectangle\:=\:15\:unit}\\\\\bullet\sf{Breadth\:of\:rectangle\:=\:12\:unit}$