Question

the area of a Rhombus is 108cm² if the length of one diagonal is 12cm what is the length of the other Diagonal?​

Answer 1

Answer:

18 centimetre

Step-by-step explanation:

let the other diagonal be x cm

area = 1/2×12×x cm =6x cm

then,

6x = 108

or, x = 108/6

also x = 18

Answer 2

AnswEr-:

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

• The area of a Rhombus is 108cm².

• The length of of Diagonal 1 is 12 cm .

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

• The length of Diagonal 2

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

$\mathrm { \longmapsto { \star{ Area \:of\: Rhombus \: = \dfrac{1}{2} \times Diagonal _{1} \times Diagonal _{2} }}}$

$\sf{\bf {Here-:}}$

• The area of a Rhombus is 108cm².

• The length of of Diagonal 1 is 12 cm .

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

• $:\implies { \mathrm {\dfrac {1}{2} \times 12 \times Diagonal _{2}= 108 cm^{2}}}$

• $:\implies { \mathrm {\dfrac {1}{\cancel {2}} \times \cancel {12} \times Diagonal _{2}= 108cm^{2}}}$

• $:\implies { \mathrm { 6 \times Diagonal _{2}= 108cm^{2}}}$

• $:\implies { \mathrm { Diagonal _{2}= \dfrac{108}{6}}}$

• $:\implies { \mathrm { Diagonal _{2}= \dfrac{\cancel {108}}{\cancel {6}}}}$

• $:\implies { \mathrm { Diagonal _{2}= 18\: cm }}$

Hence -:

• $\underline{\longmapsto { \mathrm { The\:other\:Diagonal \:or\:Diagonal _{2}\:of\:Rhombus\:= \bf{18\: cm} }}}$

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Verification ♡ -:

$\mathrm { \longmapsto { \star{ Area \:of\: Rhombus \: = \dfrac{1}{2} \times Diagonal _{1} \times Diagonal _{2} }}}$

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

• $:\implies { \mathrm {\dfrac {1}{2} \times 12 \times 18 = 108 cm^{2}}}$

• $:\implies { \mathrm {6 \times 18 = 108 cm^{2}}}$

• $:\implies { \mathrm {108 cm^{2}= 108 cm^{2}}}$

Therefore,

• L.H.S = R.H.S
• Hence, Verified

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

• Area of Rhombus = ½ × Diagonal 1 × Diagonal 2
• Area of Triangle = ½ × Base × Height
• Area of Rectangle = Length × Breadth
• Area of Square = Side × Side

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