Question

the area of a rhombus is 210cm square. if one of its diagnols is 14cm, then find its other diagnol.​

Answer 1

$\rm{ \underline{ \huge{Given: }}}$

• Area of rhombus = 210 cm²
• Diagonal 1 (d1) = 14 cm

$\rm{ \underline{ \huge{To \: \: find: }}}$

• Another diagonal (d2)

$\rm{ \underline{ \huge{ Solution: }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathfrak{ \green{ \underline{ Formula \: to \: calculate \: area \: of \: rhombus}}}$

$\boxed{ \mathfrak{ \red{ \large{ area = \frac{1}{2} \times diagonal1 \times diagonal2}}}}$

According to question,

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 14 \times d2 = 210}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: \: 14 \times d2 = 210 \times 2}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: \: d2 = \frac{210 \times 2}{14}}$

$\large{ \tt \implies \: \: \: \: \: \: \: \: \: \: d2 = 30}$

$\rm{ \underline{ \huge{Hence:}}}$

• The length of another diagonal of rhombus is 30 cm

Answer 2

$\underline\bold{Given \: that, \: }$

• $\sf \: Area \: of \: a \: rhombus \: is \: 210 {cm}^{2}.$
• $\sf \: One \: of \: its \: diagonals \: is \: 14cm.$

$\underline\bold{We \: have \: to \: find}$

• $\sf \: other \: diagonal.$

$\underline\bold{Let }$

• $\sf \: first \: diagonal \: = \bold{d1}$
• $\sf \: second \: diagonal \: = \bold{d2}$

$\sf\purple{Solution \: - }$

$\underline\bold{As \: we \: know \: that }$

$\boxed{\boxed{\bold\purple{\bigstar \: area \: of \: a \: rhombus \: = \frac{1}{2} \times d1 \times d2 }}}$

$\underline\bold{According \: to \: question \: -}$

$\sf\implies \: \frac{1}{2} \times 14 \times d2 = 210 \\ \\ \sf\implies \: \frac{14}{2} \times d2 = 210 \: \: \\ \\ \sf\implies \: \cancel\dfrac{14}{2} \: \times d2 = 210 \\ \\ \sf\implies \: 7 \times d2 = 210 \\ \\ \sf\implies \: d2 = \cancel\frac{210}{7} \\ \\ \sf\implies \: d2 = \boxed{\bold\purple{30cm}} \bigstar$

$\sf\therefore\sf\underline{Hence \: the \: other \: diagonal \: is \: \bold{30cm}.}$