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QUESTION --- (The length of a rectangle is 10 cm and its perimeter is 30 cm find its breadth..)​

Answer 1

$\frak{Given}\begin{cases}\sf{\;\;\; Length\; of \; rectangle = \bf{10\;cm}}\\\sf{\;\;\;Perimeter\:of\; rectangle = \bf{30\;cm}}\end{cases}$

Need to find:

• Breadth of the rectangle.

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

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

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• Here, l is length of the rectangle and b is breadth of the rectangle.

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Therefore,

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$:\implies\sf 2(10 + b) = 30 \\\\\\:\implies\sf 20 + 2b = 30\\\\\\:\implies\sf 2b = 30 - 20 \\\\\\:\implies\sf 2b = 10 \\\\\\:\implies\sf b = \cancel\dfrac{10}{2} \\\\\\:\implies{\underline{\boxed{\frak{\pink{b = 5\; cm}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; breadth\; of \; the \: rectangle\; is\; \bf{ 5\;cm}.}}}$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: More \ to \ know\: :}}}}\mid}$⠀

• A Quadrilateral with four sides is called as rectangle. And, opposite sides of a rectangle are parallel and are equal in length.

• Perimeter of Rectangle = 2(Length + Breadth).

• Area of a Rectangle Formula, A = (Length × Breadth).

• Diagonal of a Rectangle Formula is, $\sf D = \sqrt{(l)^2 + (b)^2}$

Answer 2

Correct Question-:

• The length of a rectangle is 10 cm and its perimeter is 30 cm . Find its breadth.

AnswEr-:

• $\underline{\boxed{\star{\sf{\pink{  Breadth \:of\:Rectangle \:is\: = 5cm.}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:Perimeter \:of\:Rectangle\:\:is\:= \frak{30cm}} & \\\\ \sf{Length \:of\:Rectangle \:is \:=\:\frak{10cm}}\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:Breadth \:of\:Rectangle\:\:.}\end{cases}$

Now ,

• $\underline{\boxed{\star{\sf{\pink{  Perimeter \:of\:Rectangle \:is\: =  2( Length + Breadth).}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:Perimeter \:of\:Rectangle\:\:is\:= \frak{30cm}} & \\\\ \sf{Length \:of\:Rectangle \:is \:=\:\frak{10cm}}& \\\\ \sf{ Breadth \:of\:Rectangle \:is \:=\:\frak{??}} \end{cases}$

Now ,

• $\implies{\sf{\large { 2(10 + Breadth) = 30 cm }}}$
• $\implies{\sf{\large { (10 + Breadth) =\frac{ 30}{2} }}}$
• $\implies{\sf{\large { 10 + Breadth = 15 }}}$
• $\implies{\sf{\large { Breadth = 15 -10 }}}$
• $\implies{\sf{\large { Breadth = 5cm }}}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{  Breadth \:of\:Rectangle \:is\: = 5cm.}}}}}$

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♤ Verification ♤

• $\underline{\boxed{\star{\sf{\blue{  Perimeter \:of\:Rectangle \:is\: =  2( Length + Breadth).}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:Perimeter \:of\:Rectangle\:\:is\:= \frak{30cm}} & \\\\ \sf{Length \:of\:Rectangle \:is \:=\:\frak{10cm}}& \\\\ \sf{ Breadth \:of\:Rectangle \:is \:=\:\frak{5cm}} \end{cases}$

Now ,

• $\implies{\sf{\large { 2(10 + 5) = 30 cm }}}$
• $\implies{\sf{\large { 2(15) = 30 cm }}}$
• $\implies{\sf{\large { 30cm = 30 cm }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{  LHS \: = RHS.}}}}}$

• $\underline{\boxed{\star{\sf{\blue{  Hence \: , Verified.}}}}}$

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| ♤ More to know ♤|

$\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}$

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Note -: Please see this answer in website [ brainly.in]

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