Question

the area of a rhombus is 510 square centimetre if one of the diagonals is 34 cm find the length of other diagonal​

Answer 1

$\huge\mathfrak\red{|☆answer☆|}$

Let the other diagonal BD be X cm. The length of the other diagonal is 30 cm.

Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf \implies Area \: of \: rhombus = 510 \: cm^{2}$

$\sf \implies Length \: of \: one \: diagonal = 34 \: cm$

$\bf \: \underline{To \: find} :$ ↴

$\sf \implies Length \: of \: other \: diagonal.$

$\bf \: \underline{Assumption} :$ ↴

$\sf \implies Let \: the \: other \: diagonal \: be \: d.$

$\bf \: \underline{Formula \: to \: be \: used} :$ ↴

$\sf\implies\boxed{\sf{ \red{Area_{(Rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}}}$

$\sf \: Where,$

$\sf\implies d_1 = Length \: of \: first \: diagonal$

$\sf \implies d_2 = Length \: of \: second \: diagonal$

$\bf \: \underline{\underline{Solution}}$

$\sf \: Putting \: the \: values,$

$\sf\implies\sf{ \dfrac{1}{2} \times 34 \times d} = 510$

$\sf\implies\sf{ 17 \times d} = 510$

$\sf\implies\sf{ 17d} = 510$

$\sf\implies\sf d = \dfrac{510}{17}$

$\sf\implies\sf d = 30 \: cm$

$\underline{ \boxed{ \pink{ \sf Hence, the \: length \: of \: other \: diagonal \: of \: rhombus = 30 \: cm.}}}$