Question

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Answer 1

Correct Question-:

• The length of a rectangle is twice to its breadth.if the perimeter is 72.6cm then, find the length and the breadth.

AnswEr -:

• $\boxed{\purple{\sf{\star{The\:length \:and\:breadth\:of\:Rectangle\:are\:24.2cm\:and\:12.1cm.}}}}$

Explanation-:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 24.2cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 12.1cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Given,

• The length of a rectangle is twice to its breadth.
• The perimeter Rectangle is 72.6cm .

To Find,

• The length and breadth of Rectangle.

Solution-:

• Let the breadth of Rectangle be X cm. .........[1]

Then ,

The length of a rectangle is twice to its breadth = 2 × x = 2x cm . ...........[2]

$\boxed{\blue{\sf{\star{Perimeter\:of\:Rectangle\:=\: 2(length+breadth)}}}}$

Here ,

• Length of Rectangle is 2x cm . ...........[ From 2]
• Breadth of Rectangle is x cm . ...........[ From 1]

Now ,

$\pink{\sf{\implies { 72.6\:cm\:=2(x + 2x)}}}$

$\pink{\sf{\implies { \frac{72.6}{2}\:=(x + 2x)}}}$

$\pink{\sf{\implies { 72.6\:cm\:=2(x + 2x)}}}$

$\pink{\sf{\implies { 36.3\:\:=x + 2x}}}$

$\pink{\sf{\implies { 36.3\:\:=3x}}}$

$\pink{\sf{\implies { x\:=\frac{36.3}{3}}}}$

$\pink{\sf{\implies { x\:=12.1}}}$

Therefore,

$\boxed{\purple{\sf{\implies { x\:=12.1}}}}$

Now ,

The length of Rectangle is 2x = 2 × 12.1 = 24.2 cm

The breadth of Rectangle is x = 12.1 cm

Hence,

$\boxed{\purple{\sf{\star{The\:length \:and\:breadth\:of\:Rectangle\:are\:24.2cm\:and\:12.1cm.}}}}$

______________________________________________________

♤| Verification |♤

$\boxed{\blue{\sf{\star{Perimeter\:of\:Rectangle\:=\: 2(length+breadth)}}}}$

Here ,

The length of Rectangle is = 24.2 cm

The breadth of Rectangle is = 12.1 cm

Now ,

$\pink{\sf{\implies { 72.6\:cm\:=2(12.1 + 24.2)}}}$

$\pink{\sf{\implies { 72.6\:cm\:=2(36.3)}}}$

$\pink{\sf{\implies { 72.6\:cm\:=72.6 cm}}}$

$\boxed{\purple{\sf{\star{Therefore ,\:LHS \:=\:RHS\:.}}}}$

$\boxed{\green{\sf{\star{Hence ,\:Verified \:\:!!\:.}}}}$

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Answer 2

HeRe IS UR AnS:

Let breath be a

Then length is 2 (a) = 2a

We know that perimetre if rectangle = 2(length + breath)

Given perimeter = 72.6 m

=>72.6m = 2( a+2a)

=> 72.6= 2a + 4a

=> 72.6= 6a

=> a = 12.1

Hence length is 2 (12.1) = 24.2m

mbreadth is a= 12.1 m

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