Question

The length of rectangle is 1/3 of its breath . if its perimeter is 64 then find the length and breadth of the rectangle ​

Answer 1

AnswEr :

• Length of rectangle = 8 m
• Breadth of rectangle = 24 m

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$\frak{Given}\begin{cases}\sf{~~~Length = \bf{\dfrac{1}{3} \times B}}\\ \\ \sf{~~~Perimeter = \bf{64 \;m}}\end{cases}$

❍ Let's say, that the length and Breadth of the rectangle be l and b m respectively.

A/Q,

• As it is given that, If the length of the rectangle is ⅓ of it's Breadth.

Therefore,

$:\implies\sf l = \dfrac{1}{3} \times b \\\\\\:\implies\sf l = \dfrac{b}{3} \\\\\\:\implies\sf b = 3l \quad\bigg\lgroup\frak Equation \; (\;I~)\bigg\rgroup$

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$\rule{250px}{.3ex}$

P E R I M E T E R :

$:\implies\sf Perimeter = 2\Big\{Length + Breadth \Big\}\\\\\\:\implies\sf 2l + 2b = 64\\\\\\:\implies\sf 2l + 2 \times 3l = 64\quad\bigg\lgroup\bf From \: Equation~ (~I~)\bigg\rgroup\\\\\\:\implies\sf 2l + 6l = 64\\\\\\:\implies\sf 8l = 64\\\\\\:\implies\sf l = \cancel\dfrac{64}{8} \\\\\\:\implies\underline{\boxed{\pmb{\frak{\purple{l = 8}}}}}\;\bigstar$

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Now, Substituting the value of ( / = 8 ) in equation ( I ) :

$:\implies\sf b = 3 \times l \\\\\\:\implies\sf b = 3 \times 8\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{b = 24}}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence,~length~and~breadth~of~rectangle~are~\textbf{8 m}~\sf{\&}~\textbf{24 m}~\sf{respectively.}}}}$

Answer 2

Given :-

The length of rectangle is 1/3 of its breath

To Find :-

Length and breadth

Solution :-

Let the breadth be b

Length = ¹/₃b

Now

Perimeter = 2(l + b)

64 = 2( ¹/₃b + b)

64/2 = b/3 + b

32 = b + 3b/3

32 = 4b/3

32 × 3 = 4b

96 = 4b

96/4 = b

24 = b

For length

Length =  ¹/₃ × 24

Length = 8 m