Question

$\large{ \frak{ \red{ \underline{Question:}}}}$
The area of a rhombus is 240 cm² and one of the diagonal is 16 cm. Find another diagonal.

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Answer 1

Given :

• The area of a rhombus is 240 cm² and one of the diagonal is 16 cm.

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To Find :

• Another diagonal ?

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SolutioN :

• Let us assume that, the x and y be the two diagonals of the rhombus.

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${\bf{\dag}}$ Formula Used :

$\qquad\star~{\underline{\boxed{\pmb{\sf{Area~of~ rhombus~=~\dfrac{d_{1}~×~d_{2}}{2}}}}}}$

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${\bf{\dag}}$ According to the Question :

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$\qquad{\sf:\implies{\dfrac{1}{2}~×~d_{1}~×~d_{2}~=~240}}$

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$~\qquad{\sf:\implies{\dfrac{1}{2}~×~16~×~x~=~240}}$

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$~~\qquad{\sf:\implies{8~×~x~=~240}}$

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$~~~\qquad{\sf:\implies{x~=~\cancel\dfrac{240}{8}}}$

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$~~~~\qquad:\implies{\pmb{\underline{\boxed{\pink{\frak{x~=~30 }}}}}}$★

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Hence,

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$\qquad$ ∴ The another diagonal is 30 cm.

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Answer 2

$\huge \mathfrak \red{☯Concept:}$

☯️We have to find the another diagonal.

$\mathfrak {\pink\bigstar \: Given : }$

➜Area of the rhombus = 240cm²

➜One of the diagonal = 16 cm

$\bf \red{To \: Find : }$

→Another diagonal.

$\boxed{ \mathfrak \red {\underline{Answer : }}}$

$\sf \: \pink Formulae \implies$

$\red{A= \frac{p \: q}{2}}$

$\sf \: diagonal \rightarrow16 \: cm$

$\sf \: area \rightarrow \: 240 {cm}^{2}$

$\sf {Solving \: for } \: \mathcal { p}$

$\mathfrak \pink{p = 2 \frac{A}{q} }$

$p = \frac{240}{16} \times 2 = 30$

$\sf \: diagonal \implies \red{30cm}$

➜So the other diagonal is 30 cm

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