Question

The perimeter of a rectangle is 75 cm. Its length is 11 times its breadth. Find the length and breadth of the rectangle.​

Answer 1

Given:

• The perimeter of a rectangle is 75 cm

• Its length is 11 times its breadth

To Find:

• The length and the breadth of the rectangle

⇨ Analysis :

here, we have given that the perimeter of the rectangle is 75cm and that length of the rectangle is 11 times greater than the breadth of the given rectangle. So, here we are going to use the concept of trasposing the values from L.H.S to R.H.S of the equation after framing it.

Solution:

${\sf{\underline{\bigstar \: According \: to \: the \: question}}}$

★ Let's Consider the Lenght now as,

• ${\bf{\pink{ 11 \times breadth }}}$

${\purple{ \underline{ \mathfrak{ As \: we \: know \: that \dag}}}}$

$\star \: \blue{ \underline{ \boxed{ \pink{ \mathfrak{ perimeter \: of \:a \: rectangle = 2(l + b)}}}}}$

Where,

• L stands for ${\bf{\pink{ Length}}}$

• B stands for ${\bf{\blue{ Breadth}}}$

${\sf{\underline {Put \: the \: given \: values}}}$

${ : \implies} \sf \: 75 = 2(11 \: b + b) \\ \\ \\ \\ { : \implies} \sf \: {75}= 2(12b )\\ \\ \\ \\ { : \implies} \sf \: 75 = 22b \\ \\ \\ \\ { : \implies} \sf \: \: b \: = \cancel{\frac{75}{2} } \\ \\ \\ { : \implies} \sf { \orange{ \underline{ \boxed{ \mathfrak{ \: b = 3.125}}}}}$

Now,

${\longrightarrow} \tt \: length \: of \: the \: rectangle \: = 3.125 \times 11 \\ {\longrightarrow} \tt \: length \: of \: the \: rectangle \: = \: 34.375cm \: \: \: \: \: \:$

━━━━━━━━━━━━━━━━━━━━━━

${\longrightarrow} \tt \: breadth \: of \: the \: rectangle \: =3.125 \times 1 \\ {\longrightarrow} \tt \: breadth \: of \: the \: rectangle \: =3.125cm$

Diagram:

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.5,2){\sf{\large{3.125 cm}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\sf{\large{34.375 cm}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$ㅤㅤ

ㅤㅤㅤ ㅤㅤㅤ ━━━━━━━━━━━━━━━━━━⠀ ㅤㅤㅤㅤㅤ ㅤㅤㅤㅤ

${ \rm{ \underline{ \therefore \: the \: dimentions \: are \: 3.125cm \: and \: 34.375cm}}}$

Answer 2

⧠ Let the breadth of the rectangle be x and length of the rectangle be 11x.

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⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bf{\dag}{\frak{\;As\;we\;know\;that\;:}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\pink{\sf{Perimeter_{(rectangle)}=2(l+b)}}}}$

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Therefore,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf{75=2(11x+x)}\\\\\\:\implies\sf{75=22x+2x}\\\\\\:\implies\sf{75=24x}\\\\\\:\implies\sf{x=\cfrac{75}{24}}\\\\\\:\implies{\underline{\boxed{\purple{\frak{x=3.125}}}}}{\;\bigstar}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Hence,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Length of the rectangle = 11x = (11 × 3.125)m = 34.375m
• Breadth of the rectangle = x = 3.125m