Question

The lenght of a rectangle is three times it's breadth.If the area of the rectangle is 1875sq.cm,find it's perimeter.answer with steps and pls give a right answer..​

Answer 1

❍ Let's Consider breadth of Rectangle be x cm .

Given that :

⠀⠀⠀⠀The lenght of a rectangle is three times it's breadth .

Then ,

• Length of Rectangle is 3x cm .

⠀⠀⠀⠀⠀Finding Length and breadth of Rectangle:

$\underline {\frak{\sf{\dag As ,\;We\;know \:that\::}}}$

• $\underline {\boxed {\sf{\star Area_{(Rectangle)} = l \times b \:sq.units}}}$

Where ,

• l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm .

$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ x \times 3x = 1875 cm^{2} }\\\\ :\implies \sf{ 3x^{2} = 1875 cm^{2} }\\\\ :\implies \sf{ 3x^{2} = \dfrac{\cancel {1875}}{\cancel {3}} }\\\\ :\implies \sf{ x^{2} = 625 }\\\\ :\implies \sf{ x = \sqrt {625} }\\\\\underline {\boxed{\pink{ \mathrm {  x = 25\: cm}}}}\:\bf{\bigstar}$

Therefore,

• Breadth of Rectangle is x = 25 cm .
• Length of Rectangle is 3x = 3 × 25 = 75 cm .

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Length \;and\;Breadth \:of\:Rectangle \:are\:\bf{25\: cm\:and\:75cm\:}\:respectively}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Finding Perimeter of Rectangle:

$\underline {\frak{\sf{\dag As ,\;We\;know \:that\::}}}$

• $\underline {\boxed {\sf{\star Perimeter _{(Rectangle)} =2( l + b) \:units}}}$

Where ,

• l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm .

$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ Perimeter_{(Rectangle)} = 2 (25 + 75) }\\\\ :\implies \sf{ Perimeter_{(Rectangle)} = 2 (100) }\\\\ :\implies \sf{ Perimeter_{(Rectangle)} = 2\times 100 }\\\\ \underline {\boxed{\pink{ \mathrm {  Perimeter _{(Rectangle)} = 200\: cm}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Perimeter \:of\:Rectangle \:is\:\bf{200cm\:}\:respectively}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}$

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

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