Question

13. Length of a rectangle is 2 cm more than twice its breadth. If the perimeter of the rectangle is 34



cm, find its length and breadth.





​

Answer 1

Given : Length of a Rectangle is 2 cm more than twice it's breadth & the perimeter of the rectangle is 34 cm .

Exigency To Find : The Length and Breadth of Rectangle .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider Breadth of Rectangle be x cm

⠀⠀⠀⠀⠀Given that ,

》Length of a Rectangle is 2 cm more than twice it's breadth .

Therefore,

• Length of Rectangle is ( 2 + 2x ) cm

As , We know that ,

$\qquad \dag\:\:\bigg\lgroup \pmb{ Perimeter _{(Rectangle)} \:=\:2\:(\:Length \:+ \:Breadth \:)\: }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , Length of Rectangle is x cm , Breadth of Rectangle is ( 2x + 2 ) cm & Perimeter of Rectangle is 34 cm.

$\dashrightarrow \sf \:2\:(\:Length \:+ \:Breadth \:)\: =\:Perimeter \:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\dashrightarrow \sf \:2\:(\:Length \:+ \:Breadth \:)\: =\:Perimeter \:\\\\ \dashrightarrow \sf \:2\:\bigg( \:(\:2x +\: 2\:)\: \:+ \:x \:\bigg)\: =\:34 \:\\\\ \dashrightarrow \sf \:2\:\:(\:2x +\: 2\:)\: \:+ 2\:(x) \:\: =\:34 \:\\\\ \dashrightarrow \sf \:\:4x +\: 4\:\: \:+ 2x \:\: =\:34 \:\\\\ \dashrightarrow \sf \:\:6x +\: 4\:\: \: \:\: =\:34 \:\\\\ \dashrightarrow \sf \:\:6x \:\: =\:34 - 4\:\\\\ \dashrightarrow \sf \:\:6x \:\: =\:30\:\\\\ \dashrightarrow \sf \:\:x \:\: =\:\cancel {\dfrac{30}{6}}\:\\\\ \dashrightarrow \sf \:\:x \:\: =\:5\:\\\\ \qquad \therefore \pmb{\underline{\purple{\:x =\:\:5 }} }\:\:\bigstar$

⠀⠀⠀⠀⠀Therefore,

• Length of Rectangle is ( 2x + 2 ) = ( 2 × 5 + 2 ) = ( 10 + 2 ) = 12 cm .
• Breadth of Rectangle is x = 5 cm

$\qquad \underline {\sf Hence, \:\:Length \:and \:Breadth \:of\:Rectangle \:are \: \bf 12 \:cm \:\&\: 5 \:cm \:\sf , respectively \:.}$