Question

the area of rectangular park is same as the area of sqaure park.if the length of rectangular park is 40m and side of sqaure park is 80m. find the length of rectangular park.​

Answer 1

ᴀɴsᴡᴇʀ :

♡Reference of Image is shown in diagram

$\setlength{\unitlength}{1.5cm}\begin{picture}(20,2)\thicklines\put(7.4,2){\mathsf{\large{80 m}}}\put(9.2,0.7){\matsf{\large{}}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(14.1,1.6){\mathsf{\large{}}}\put(12.7,0.7){\matsf{\large{50 cm}}}\put(12,1){\line(1,0){2}}\put(12,1){\line(0,2){1.5}}\put(14,1){\line(0,3){1.5}}\put(12,2.5){\line(3,0){2}}\put(9,1.8){\Large\rm Rectangle }\put(12.3,1.6){\rm Square}\end{picture}$

$\rule{170}2$

☯ $\large\underline{\textsf{Area \: of \: Rectangular \: park:}}$

$\normalsize\bigstar\:{\boxed{\sf{Area \: of \: rectangle = Length \times\ Breadth}}}$

$\normalsize\dashrightarrow\quad\sf\ Area_{rectangle} = Length \times\ 40$

$\normalsize\dashrightarrow\quad{\underline{\boxed{\sf{Area_{rectangle} = (Length \times\ 40)\:m^2}}}}$

☯ $\large\underline{\textsf{Area \: of \: Square \: park:}}$

$\normalsize\bigstar\:{\boxed{\sf{Area \: of \: square = (side)^2}}}$

$\normalsize\twoheadrightarrow\quad\sf\ Area_{square} = 80 \times\ 80$

$\normalsize\twoheadrightarrow\quad\sf\ Area_{square} = 6400$

$\normalsize\twoheadrightarrow\quad{\underline{\boxed{\sf{Area_{square} = 6400 \: m^2}}}}$

$\rule{100}1$

☯ $\large\underline{\textsf{It \: is \: given \: that:}}$

$\normalsize\bigstar\:{\boxed{\sf{Area \: of \: square \: park = Area \: of \: rectangular \: park }}}$

$\normalsize\ : \implies\quad\sf\ Area_{square} = Area_{square}$

$\normalsize\ : \implies\quad\sf\ 6400 = (Length \times\ 40)$

$\normalsize\ : \implies\quad\sf\frac{\cancel{6400}}{\cancel{40}} = Length$

$\normalsize\ : \implies\quad\sf\ Length = 160$

$\normalsize\ : \implies\quad{\underline{\boxed{\sf \red{Length = 160 \: m}}}}$

$\therefore\:\underline{\textsf{Hence, \: the \: length \: of \: rectangular \: park \: is}{\textbf{\: 160m}}}$

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer = 160 m

$\rule{110}1$

$\huge\sf\blue{Given}$

➝ Area of a square = Area of a square

➝ Breadth of the rectangular park = 40 m

➝ Side of the square = 80 m

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

✭ The length of the rectangle?

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$\huge\sf\purple{Steps}$

❍ $\large\underline{\textsf{Area\:of\:Rectangular\:park:}}$

$\normalsize\bullet\underline{\boxed{\sf{Area \: of \: rectangle = Length \times\ Breadth}}}$

$\normalsize\dashrightarrow\quad\sf\ Area_{rectangle} = Length \times\ 40$

$\normalsize\dashrightarrow\quad{\underline{\boxed{\sf{Area_{rectangle} = (Length \times\ 40)\:m^2}}}}$

❍ $\large\underline{\textsf{Area \: of \: Square \: park:}}$

$\normalsize\bullet\underline\:{\boxed{\sf{Area \: of \: square = (side)^2}}}$

$\normalsize\twoheadrightarrow\quad\sf\ Area_{square} = 80 \times\ 80$

$\normalsize\twoheadrightarrow\quad\sf\ Area_{square} = 6400 m$

❍ $\large\underline{\textsf{Given \: that:}}$

$\normalsize\bullet\underline\:{\boxed{\sf{Area \: of \: square \: park = Area \: of \: rectangular \: park }}}$

$\normalsize \dashrightarrow\quad\sf\ Area_{square} = Area_{square}$

$\normalsize\dashrightarrow\quad\sf\ 6400 = (Length \times\ 40)$

$\normalsize\dashrightarrow\quad\sf\dfrac{{6400}}{{40}} = Length$

$\normalsize \dashrightarrow\quad\sf\ Length = 160$

$\normalsize \dashrightarrow\quad{\underline{\boxed{\sf \red{Length = 160 \: m}}}}$

$\rule{170}3$