Question

4. The ratio of sides of a rectangle is 3 : 4. If its area is 300 m², find its perimeter ? will​

Answer 1

Answer:

Answer :

• ➝ Perimeter of rectangle is 70 m.

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Right Question :

The ratio of sides of a rectangle is 3 : 4. If its area is 300 m², find its perimeter?

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Given :

• ➝ Radio of side of rectangle = 3:4
• ➝ Area of rectangle = 300 m².

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To Find :

• ➝ Perimeter of rectangle

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Using Formula :

• ➝ Area of rectangle = l × b
• ➝ Perimeter of rectangle = 2(l + b)

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Solution :

$\bull \: \underline{\underline{\sf{\red{Assume,}}}}$

• ➝ Length of rectangle = 3x
• ➝ Breadth of rectangle = 4x

$\bull \: \underline{\underline{\sf{\red{According \: to \: the \: question,}}}}$

$\dashrightarrow\tt{Area \: of \: rectangle = l \times b}$

$\dashrightarrow\tt{300 = 3x \times 4x}$

$\dashrightarrow\tt{300 = 12{x}^{2}}$

$\dashrightarrow\tt{{x}^{2}=\dfrac{300}{12} }$

$\dashrightarrow\tt{{x}^{2}= \cancel{\dfrac{300}{12}}}$

$\dashrightarrow\tt{{x}^{2}= 25}$

$\dashrightarrow\tt{x= \sqrt{25} }$

$\dashrightarrow\tt{x=5 }$

• ➝ Hence, the value of x is 5.

$\bull \: \underline{\underline{\sf{\red{Hence,}}}}$

• ➝ Length = 3x = 3×5 = 15 m
• ➝ Breadth = 4x = 4×5 = 20 m

$\bull \: \underline{\underline{\sf{\red{Finding \: the \: perimeter \: of \: rectangle,}}}}$

${\dashrightarrow{\tt{Perimeter_{(Rectangle)} = 2(l + b)}}}$

${\dashrightarrow{\tt{Perimeter_{(Rectangle)} = 2(15+20)}}}$

${\dashrightarrow{\tt{Perimeter_{(Rectangle)} = 2(35)}}}$

${\dashrightarrow{\tt{Perimeter_{(Rectangle)} = 2 \times 35}}}$

${\dashrightarrow{\tt{Perimeter_{(Rectangle)} = 70 \: m}}}$

• ➝ Hence, the perimeter of rectangle is 70 m.

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Learn More :

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

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