Question

If the diagonals of the Rhombus are in the ratio 4:7 and the area is 504sqcm. Find the
length of the diagonals.​

Answer 1

Hope this helps And welcome

Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf\implies The \: diagonals \: of \: the \: rhombus \: are \: in \: the \: ratio \: 4 : 7$

$\sf\implies The \: area \: of \: the \: rhombus = 504 \: cm ^{2}$

$\bf \: \underline{To \: find} :$ ↴

$\sf\implies The \: length \: of \: the \: diagonals.$

$\bf \: \underline{Let \: us \: assume, }$

$\sf \implies Smaller \: diagonal \: be \: 4x$

$\sf \implies Bigger \: diagonal \: be \: 7x$

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

$\sf \implies \boxed{ \pink{ \sf \: Area \: of \: rhombus = \dfrac{D_1 \times D_2}{2} }}$

$\sf \: Where,$

$\sf \implies D_1 = Smaller \: diagonal$

$\sf \implies D_2 = Bigger \: diagonal$

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

$\sf \implies \sf \dfrac{4x \times 7x}{2} = 504$

$\sf \implies \sf \dfrac{28x^{2} }{2} = 504$

$\sf \implies \sf 28x ^{2} = 504 \times 2$

$\sf \implies \sf 28x ^{2} = 1008$

$\sf \implies \sf x ^{2} = \dfrac{1008}{28}$

$\sf \implies \sf x ^{2} = 36$

$\sf \implies \sf x ^{2} = 6 ^{2}$

$\sf \implies \sf x = 6$

$\sf \: So, diagnolas \: of \: the \: rhombus \: are :$ ↴

$\sf \implies \sf Smaller \: diagonal = 4x = (4 \times 6) = 24 \: cm$

$\sf \implies \sf Bigger \: diagonal = 7x =( 7 \times 6)= 42 \: cm$