Question

Perimetreof a rectangle is 80 metres and its length is one metre more than twice the breadth so what is the length and breadt

Answer 1

QuestioN :

Perimeter of a rectangle is 80 metres, and its length is one metre more than twice the breadth so what is the length and breadth.

GiveN :

• Perimeter of rectangle = 80 m
• Breadth of Perimeter is 1 m long than twice it's length.

To FinD

• Length and Breadth

SolutioN :

Let, the breadth be x. and length be y

Then length will be

⇒y = 2x + 1.....(1)

$\underbrace{\sf{Perimeter \: of \: Rectangle}} \\ \\ \implies \sf{Perimeter \: = \: 2(length \: + \: Breadth)} \\ \\ \implies \sf{Perimeter \: = \: 2(x \: + \: 2x \: + \: 1)} \\ \\ \implies \sf{80 \: = \: 2(3x \: + \:1)} \\ \\ \implies \sf{80 \: = \: 6x \: + \: 2} \\ \\ \implies \sf{6x \: = \: 80 \: - \: 2} \\ \\ \implies \sf{6x \: = \: 78} \\ \\ \implies \sf{x \: = \: \dfrac{\not{78}}{\not{6}}} \\ \\ \implies \sf{x \: = \: 13} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \bullet \: Breadth \: of \: Rectangle \: is \: 13 \: m}$

Put value of x in (1)

$\implies \sf{y \: = \: 2(13) \: + \: 1} \\ \\ \implies \sf{y \: = \: 26 \: + \: 1} \\ \\ \implies \sf{y \: = \: 27} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \bullet \: Length \: of \: rectangle \: is \: 27 \: m}$

Answer 2

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\: breadth\:of\: rectangle=x\:m}$
• $\rm{The\: length\:of\: rectangle=2x+1\:m}$

$\small{\underline{\green{\rm{Given:}}}}$

• $\rm{The\: perimeter\:of\: rectangle=80\:m}$

$\small{\underline{\green{\rm{To\: Find:}}}}$

• $\rm{The\: breadth\:and\: length\:of\: rectangle=?}$

$\small{\underline{\orange{\rm{According\: to\:the\: Question:}}}}$

$\rm\orange{\implies Perimeter=2(l+b)}$

$\rm{\implies 2(2x+1+x)=80}$

$\rm{\implies 2(3x+1)=80}$

$\rm{\implies 6x+2=80}$

$\rm{\implies 6x=80-2}$

$\rm{\implies 6x=78}$

$\rm\red{\implies x=13}$

Hence,

$\rm{\implies The\: length\:of\: rectangle=2x+1=2*13+1=27\:m}$

$\rm{\implies The\: breadth\:of\: rectangle=13\:m}$

$\huge{\underline{\purple{\rm{Verification:}}}}$

$\rm\orange{\implies Perimeter=2(l+b)}$

$\rm{\implies 2(27+13)=80}$

$\rm{\implies 2*40=80}$

$\rm{\implies 80=80}$

$\rm\red{\implies Hence,\:Verified}$