Question

If Length of dingonal of a rhombers whose area is 264 length is 24 cm. then find the length of second diagnol​

Answer 1

$\boxed{\huge{\bf{\star{Correct\:question \:-:}}}}$

• If the length of diagonal of a rhombus whose area is 264 cm² length is 24 cm. then Find the length of second Diagonal.

AnswEr-:

• $\underline{\boxed{\sf{\large { Diagonal_{2}\:or\:The\:second \:diagonal\:of\:Rhombus\:is\:22\:cm}}}}$

Explanation-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\: \:Diagonal \:of\:\:Rhombus \:is\:= \frak{24cm}} & \\\\ \sf{Area \:of\:Rhombus \:is \:=\:\frak{264cm^{2}}}\end{cases}$

• $\frak{To \:Find \:\: -:} \begin{cases} \sf{The\:second \:Diagonal \:of\:\:Rhombus \:}\end{cases}$

$\star {\bigstar {\sf{\large { Solution \:of\:Question -: }}}}$

• $\underline{\boxed{\star{\sf{\purple{Area\:of \:Rhombus\::\dfrac {1}{2} \times Diagonal_{1} \times Diagonal_{2}}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{Diagonal _{1}\:=\:First \:Diagonal \:of\:\:Rhombus \:is\:= \frak{24cm}} & \\\\ \sf{Area \:of\:Rhombus \:is \:=\:\frak{264cm^{2}}}& \\\\\sf{Diagonal _{2}=\:Second \:Diagonal \:of\:\:Rhombus \:is\:= \frak{??}} \end{cases}$

$\star {\bigstar {\sf{\large { Now -: }}}}$

• $\longrightarrow{\sf{\large { 264cm^{2}= \dfrac{1}{2} \times 24 \times Diagonal_{2} }}}$

• $\longrightarrow{\sf{\large { 264cm^{2}= 12 \times Diagonal_{2} }}}$

• $\longrightarrow{\sf{\large { \dfrac{264}{12} = Diagonal_{2} }}}$

• $\longrightarrow{\sf{\large { 22cm = Diagonal_{2} }}}$

$\star {\bigstar {\sf{\large { Hence -: }}}}$

• $\underline{\boxed{\sf{\large { Diagonal_{2}\:or\:The\:second \:diagonal\:of\:Rhombus\:is\:22\:cm}}}}$

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$\star {\bigstar {\sf{\huge { Verification -: }}}}$

• $\underline{\boxed{\star{\sf{\purple{Area\:of \:Rhombus\::\dfrac {1}{2} \times Diagonal_{1} \times Diagonal_{2}}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{Diagonal _{1}\:=\:First \:Diagonal \:of\:\:Rhombus \:is\:= \frak{24cm}} & \\\\ \sf{Area \:of\:Rhombus \:is \:=\:\frak{264cm^{2}}}& \\\\\sf{Diagonal _{2}=\:Second \:Diagonal \:of\:\:Rhombus \:is\:= \frak{22cm}} \end{cases}$
• $\star {\bigstar {\sf{\large { Now \:Putting\:known\:Values-: }}}}$

• $\longrightarrow{\sf{\large { 264cm^{2}= \dfrac{1}{2} \times 24 \times 22 }}}$

• $\longrightarrow{\sf{\large { 264cm^{2}= 12 \times 22 }}}$

• $\longrightarrow{\sf{\large { 264cm^{2}= 264cm^{2} }}}$

Therefore,

• $\implies {\bigstar {\sf{\large {LHS = RHS }}}}$

• $\implies {\bigstar {\sf{\large {Hence ,\:Verified}}}}$

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