Question

The length of a rectangle is 3m less than twice the width, and the area of ​​the rectangle is 65m. Find the dimensions of the rectangle.

Answer 1

Given that , The Length of Rectangle is 3 less than twice the width of Rectangle and Area of Rectangle is 65 m² .

Exigency To Find : The Length & Width of Rectangle ?

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❍ Let's say that Width of Rectangle be x m and Length of Rectangle be ( 2x - 3 ) m , i.e. Length of Rectangle is 3 less than twice the width of Rectangle .

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⠀⠀▪︎ We've the expressions for the Length and Width of Rectangle . We'll find the actual value of Length and Width of Rectangle using formula to find Area of Rectangle .

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》 Formula for Area of Rectangle is Given by — :

$\\\qquad \qquad \star \:\:\underline{ \boxed {\pmb{\frak{ \:\:Area\:_{(\:Rectangle \:)}\:=\:\big( Length \big) \:\times \:\big(\:Width \:\big)\:\:sq.units \:}}}}\:$

$\dag\:\underline {\frak{ Putting \:\:known \:\:Values \:\:in \:\:Formula \:\::}}$

$:\implies \sf \:\:Area\:_{(\:Rectangle \:)}\:=\:\Big\{ Length \Big\} \:\times \:\Big\{\:Width \:\Big\}\:\\\\\\ :\implies \sf \:\:65\:=\:\Big\{ 2x - 3 \Big\} \:\times \:\Big\{\:x \:\Big\}\:\\\\\\ :\implies \sf \:\:65\:=\:x\:\Big\{ 2x - 3 \Big\} \:\:\\\\\\ :\implies \sf \:\:65\:=\:\:2x^2 - 3x \:\:\\\\\\ :\implies \sf \:\:\:\:2x^2 - 3x - 65 \:=\:0 \:\:\\\\\\ :\implies \sf \:\:\:\:2x^2 - 13x + 10x - 65 \:=\:0 \:\:\\\\\\ :\implies \sf \:x\: \Big\{ 2x - 13 \Big\} \:+\:5\: \Big\{ 2x - 13 \Big\} \: \:=\:0 \:\:\\\\\\ :\implies \sf \: \Big\{ x + 5 \Big\} \: \Big\{ 2x - 13 \Big\} \: \:=\:0 \:\:\\\\\\ :\implies \underline {\boxed {\pmb{\frak{\purple { x \:\:=\:\:-5 \:\:\:or\:\:\:\dfrac{13}{2}\:\:}}}}}\:\:\bigstar \:\:$

As , We know that ,

• Dimensions can't be in –ve , So ignoring –ve value of x we get , x = 13/2 = 6.5 metres

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Therefore,

• Length of Rectangle is , x = 6.5 m
• Width of Rectangle is , ( 2x - 3 ) = [ 2(6.5) - 3 ] = 13 - 3 = 10 m

$\\\qquad \therefore \:\underline {\sf \:Hence, \:Dimensions \:of \:Rectangle \:are \:\pmb{\sf 10 \:m \:}\:and \:\pmb{\sf 6.5 \:m \:}\:,respectively \:.}$