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

$\tt\huge\underline\red{Answer:-}$

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

A/Q,

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

Therefore,

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

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

$\large\underline\bold\red{Perimeter:-}$

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

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

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

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

$\rule{300px}{.5ex}$

Answer 2

$\sf{\huge{\underline{\green{Given :-}}}}$

• The length of rectangle is 1/3 of its breath.

• The perimeter of rectangle is 64 units .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The length and breadth of the rectangle .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

The length of rectangle is 1/3 of its breath.

Let the breadth be x

So, The length of rectangle = 1/3x

The perimeter of rectangle is 64 units.

We know that, The perimeter of rectangle = 2 ( L + B )

➝ 2 ( L + B ) = 64

➝ 2 ( 1/3x + x ) = 64

➝ 1/3x + x = 64 /2

➝ 1/3x + 3/3x = 32

➝ 4/3x = 32

➝ x = 32 × 3/4

➝ x = 8 × 3

➝ x = 24

• The breadth = x = 24 units

• The length of rectangle = 1/3x = 1/3 × 24 = 8 units

$\sf{\huge{\underline{\green{Verification :-}}}}$

The perimeter of rectangle = 2 ( L + B )

➝ 2 ( L + B ) = 64

➝ 2 ( 8 + 24 ) = 64

➝ 16 + 48 = 64

➝ 64 = 64