Question

area of a rhombus is 100 sqcm and the length of one diagonal is 10 cm find the length of other diagonal​

Answer 1

AnswEr -:

• $\underline {\mathrm {\star{\pink{The\:Length \:of\:Diagonal _{2} \:or\:other \:Diagonal \:of\:Rhombus \;is\:20\:cm\:.}}}}$

Explanation-:

$\mathrm {\bf{ Given \:-:}}$

• Area of Rhombus is = 100 cm²

• Diagonal 1 or One Diagonal of Rhombus is 10 cm .

$\mathrm {\bf{ To\:Find \:-:}}$

• Diagonal 2 or Other Diagonal of Rhombus.

$\mathrm {\bf{\dag{ Solution \:of\:Question \:-:}}}\:$

$\underbrace {\mathrm {\bf{ Understanding \:the\:Concept \:-:}}}$

• We have to find Diagonal 2 [ Other Diagonal ] of Rhombus when Area and Diagonal 1 of Rhombus.

• Firstly Put the known Values [ Area and Diagonal 1 of Rhombus ] in the Formula for Area of Rhombus.

• By Putting this we can get the Diagonal 2 or Other Diagonal of Rhombus.

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$\mathrm {\bf{\dag{ Finding \: Diagonal _{2} \:or\:Other\:Diagonal \:of\:Rhombus \:-:}}}\:$

As , We know that,

• $\underline{\boxed{\star{\sf{\red{ Area_{(Rhombus)}  \: = \dfrac{1}{2} \times Diagonal _{1} \times Diagonal _{2} \: sq.units }}}}}$

• $\mathrm{\bf{\blue {Here \:\: -:}}} \begin{cases} \sf{\blue{The\:Diagonal _{1} \:or\:one\:Diagonal \:of \:the\:Rhombus \: \:is\:= \frak{10\:cm}}} & \\\\ \sf{\red{Area \:of\:Rhombus \:is \:=\:\frak{100cm^{2} }}}& \\\\\sf{\pink{The\:Diagonal _{2} \:or\:other\:Diagonal \:of \:the\:Rhombus \: \:is\:= \frak{\:??}}} \end{cases}$

Now By Putting known Values in Formula for Area of Rhombus-:

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { \dfrac{1}{2} \times 10 \times Diagonal _{2} = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { \dfrac{1}{\cancel {2}} \times \cancel {10} \times Diagonal _{2} = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 5 \times Diagonal _{2} = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { Diagonal _{2} = \dfrac{100}{5} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { Diagonal _{2} = \dfrac{\cancel {100}}{\cancel{5}} }}$

• $\qquad \quad \qquad \quad \underline {\boxed{\pink{\mathrm { Diagonal _{2} = 20\:cm }}}}$

Hence ,

• $\underline {\mathrm {\star{\pink{The\:Length \:of\:Diagonal _{2} \:or\:other \:Diagonal \:of\:Rhombus \;is\:20\:cm\:.}}}}$

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$\Large {\mathrm {Verification \:\red{♡}-:}}$

As , We know that,

• $\underline{\boxed{\star{\sf{\red{ Area_{(Rhombus)}  \: = \dfrac{1}{2} \times Diagonal _{1} \times Diagonal _{2} \: sq.units }}}}}$

• $\mathrm{\bf{\blue {Here \:\: -:}}} \begin{cases} \sf{\blue{The\:Diagonal _{1} \:or\:one\:Diagonal \:of \:the\:Rhombus \: \:is\:= \frak{10\:cm}}} & \\\\ \sf{\red{Area \:of\:Rhombus \:is \:=\:\frak{100cm^{2} }}}& \\\\\sf{\pink{The\:Diagonal _{2} \:or\:other\:Diagonal \:of \:the\:Rhombus \: \:is\:= \frak{\:20\:cm}}} \end{cases}$

Now By Putting known Values in Formula for Area of Rhombus-:

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { \dfrac{1}{2} \times 10 \times 20 = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { \dfrac{1}{\cancel {2}} \times \cancel {10} \times 20 = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 5 \times 20 = 100cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 100cm^{2} = 100cm^{2} }}$

Therefore,

• $\qquad \quad \qquad \quad:\implies {\mathrm { L.H.S = R.H.S }}$

• $\qquad \quad \qquad \quad:\implies {\mathrm { Hence \:, Verified \:! }}$

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$\large { \boxed {\mathrm |\:\:{\underline {More \:To\:Know\:-:}}\:\:|}}$

• Area of Rectangle = Length × Breadth sq.units

• Area of Square = Side × Side sq.units

• Area of Triangle = ½ × Base × Height sq.units

• Area of Trapezium = ½ × Height × ( a +b ) or Sum of Parallel sides sq.units

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Answer 2

Answer:

QUESTION

area of a rhombus is 100 sqcm and the length of one diagonal is 10 cm find the length of other diagonal.

ANSWER

$\fbox \green{area \: of \: rhombus} \: = 100 \: sq.cm \\ \\ \pink{ \frac{1}{2} \times 8 \times d_{2} = 100} \\ \\ \blue{8 \times d_{2} = 100 \times 2} \\ \\ \red{d_{2} = \frac{100 \times 2}{8} = 25cm}$

I hope it helps you

#SILENT GIRL ANSWER