Question

The diagonals of a rhombus are in ratio 3:4 if the longer diagonal is 12cm then find the are of rhombus​

Answer 1

Answer:

${\large{\underline{\underline{\bf{Given: -}}}}}$

• ↝ The diagonals of a rhombus are in ratio 3:4.
• ↝ The longer diagonal is 12cm

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{To \: Find: -}}}}}$

• ↝ The area of rhombus

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Using \: Formula: -}}}}}$

$\bigstar{\underline{\boxed{\bf{\purple{Area\:of\:rhombus=\dfrac{1}{2}\times{d_1}\times{d_2}}}}}}$

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Solution: -}}}}}$

$\green\bigstar$ Let the,

• ↠ The smaller diognal of rhombus = 3x
• ↠ The longer diagonal of rhombus = 4x

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Now, According to the question

$\dashrightarrow{\sf{4x = longer \: diagonal }}$

$\dashrightarrow{\sf{4x =12 }}$

$\dashrightarrow{\sf{x = \dfrac{12}{4}}}$

$\dashrightarrow{\sf{x = {\cancel{\dfrac{12}{4}}}}}$

$\dashrightarrow{\sf{x = 3}}$

$\bigstar\red{\underline{\boxed{\bf{x = 3}}}}$

∴ The value of x is 3.

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Finding the longer diagonal of rhombus :-

${\dashrightarrow{\sf{Longer \: diagonal \: of \: rhombus = 4x}}}$

${\dashrightarrow{\sf{Longer \: diagonal \: of \: rhombus = 4 \times 3}}}$

${\dashrightarrow{\sf{Longer \: diagonal \: of \: rhombus = 12 \: cm}}}$

$\bigstar{\red{\underline{\boxed{\bf{Longer \: diagonal \: of \: rhombus = 12 \: cm}}}}}$

∴ The longer diagonal of rhombus is 12 cm.

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Finding the smaller diognal of rhombus :-

$\dashrightarrow\sf{Smaller \: diognal \: of \: rhombus = 3x}$

${\dashrightarrow{\sf{Smaller \: diognal \: of \: rhombus = 3 \times 3}}}$

${\dashrightarrow{\sf{Smaller \: diognal \: of \: rhombus = 9 \: cm}}}$

$\bigstar{\red{\underline{\boxed{\bf{Smaller \: diognal \: of \: rhombus = 9 \: cm}}}}}$

∴ The smaller diognal of rhombus is 9 cm.

$\begin{gathered}\end{gathered}$

$\green\bigstar$ Now, Finding the area of rhombus :-

${\dashrightarrow{\sf{Area\:of\:rhombus=\dfrac{1}{2}\times{d_1}\times{d_2}\:}}}$

${\dashrightarrow{\sf{Area\:of\:rhombus=\dfrac{1}{2}\times 9\times 12\:}}}$

${\dashrightarrow{\sf{Area\:of\:rhombus=\dfrac{1 \times 9 \times 12}{2}}}}$

${\dashrightarrow{\sf{Area\:of\:rhombus=\dfrac{108}{2}}}}$

${\dashrightarrow{\sf{Area\:of\:rhombus= \cancel{\dfrac{108}{2}}}}}$

${\dashrightarrow{\sf{Area\:of\:rhombus=54 \: {cm}^{2} }}}$

$\bigstar{\red{\underline{\boxed{\bf{Area\:of\:rhombus=54 \: {cm}^{2}}}}}}$

∴ The area of rhombus is 54 cm².

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Learn \: More: -}}}}}$

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

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\bf{Request: -}}}}}$

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