Question

★ Math Problem !!

Let's make a rectangular garden of $\sf{\red{Length}}$ twice its $\sf{\red{Breadth}}$ . The area of the Garden measures upto 800 m² . Check whether the given design is possible or not ?

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Answer 1

Answer:

Sol. let length of rectangular garden = l m

and breadth of rectangular garden = b m

Ar. of rectangular garden = 800 m²

We know, Ar. of rectangle = l×b

According to question :

l = 2b

=> Ar. = 2b×b = 2b² m²

=> 800 = 2b²

=> b = 20m

=> l = 2×20 = 40m

So, given condition is possible if length = 40m and breadth = 20m

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt Let's\: make \: a \:rectangular \: garden \: of {\sf{\red{Length}}}\:twice\\\tt its \: {\sf{\red{Breadth}}}. \:The \: area \: of \:the \: Garden \: measures\\\tt upto \: 800 \: {m}^{2}. \:Check \:whether \: the \: given \: design\\\tt is \: possible \: or \: not?$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf Area \:of \:the \:garden(A) =800\:{m}^{2}$
• $\bf Length(l)\:of\:garden\:is\:twice\:the \:breadth(b) \:of\:the \:garden$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf The\: given\: design\: is \:possible\: or\: not \:to \:make\: a\: garden$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Length \:and\:Breadth \:of\:the \:garden}}}}}$

${\orange {\mathfrak {Let,}}}$

${\blue {\tt {\: \: \: \: \: \: \:Breadth(b) \: of \: the \: garden \: be \: x}}}$

${\blue {\tt {\: \: \: \: \: \: \:Length(l) \: of \: the \: garden \: be \: 2x}}}$

${\orange {\boxed {\boxed {\boxed {\green {\pmb {A_{(Rectangle)}=l \times b}}}}}}}$

• $\sf A=area \:of \:the \:rectangle$
• $\sf l=length\:of \:the \:rectangle$
• $\sf b=breadth\:of \:the \:rectangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 800=2x \times x$

$\bf \implies 800=2{x}^{2}$

$\bf \implies {x}^{2}=\dfrac{800}{2}$

$\bf \implies {x}^{2}=\dfrac{\cancel{800}}{\cancel{2}}$

$\bf \implies {x}^{2}=400$

$\bf \implies x=\sqrt{400}$

$\implies{\orange {\boxed {\boxed {\purple {\sf x=20\:m}}}}}$

————————————————————————————

${\tt {\blue {Breadth \:of \:the\: garden (b) =x}}}$

$\implies {\orange {\boxed {\boxed {\purple {\mathfrak {b=20\:m}}}}}}$

————————————————————————————

${\tt {\blue {Length \:of\: the\: garden (l) =2x}}}$

$\bf \implies l=2 \times 20$

$\implies {\orange {\boxed {\boxed {\purple {\mathfrak {l=40\:m}}}}}}$

${\underbrace {\red {\overline {\red {\underline {\red {\sf {\pmb {{\therefore} The\:given \:design \:is \: possible\:to\:make\:a\:garden \:when\:its\:breadth \:is\:20\:m\:and\:length \:is \:40\:m}}}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

___________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Area\:of \:the \:rectangle =l \times b$

$\sf Perimeter \:of \:the \:rectangle =2(l+b)$

$\sf Diagonall\:of \:the \:rectangle =\sqrt{{b}^{2}+{l}^{2}}$