Question

Area of a rhombus is 432 cm². If the measure of one of its diagonals is 36 cm, then find the measure of the other diagonal. ​

Answer 1

Answer:

area of rhombus= product of both diagonals

432cm²=36×x

432÷36 =x

x=12

So, the measure of other diagonal is 12cm

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Answer 2

Given : Area of the Rhombus is 432 cm² .Measure of 1 diagonal is 36 cm .

To Find : Find the Measure of 2nd Diagonal

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SolutioN : For Solving this question let's apply the formula for Area of Rhombus . Let's Solve :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Rhombus)}} = \dfrac{1}{2} \times D_1 \times D_2 }}}}}$

Where :

• $\sf{ D_1 }$ = Diagonal 1
• $\sf{ D_2 }$ = Diagonal 2

$\maltese$ Calculating the 2nd Diagonal :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = \dfrac{1}{2} \times D_1 \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 432 = \dfrac{1}{2} \times 36 \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 432 = \dfrac{36}{2} \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 432 = \cancel\dfrac{36}{2} \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 432 = 18 \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \dfrac{432}{18} = D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \cancel\dfrac{432}{18} = D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Diagonal \; 2 = 24 \; cm }}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ 2nd Diagonal of the Rhombus is 24 cm .

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