Question

The area of the rhombus is 84 square cm and its perimeter is 56 cm. Find its height.

Answer 1

sides of rhombus are equal so
perimeter =4 x side
56= 4 x side
side = 56/4
side = 14
area of rhombus = Base x height
84 = 14 x height
height = 84 /14
height = 6cm


hope it helps

Answer 2

Given:

☘︎ Area of a rhombus = 84 cm²

☘︎ Perimeter of rhombus = 56 cm

$\orange{\large{\underline{\underline{ \rm{To \: Find: }}}}} </p><p>$

❁ The height of rhombus.

$\orange{\large{\underline{\underline{ \rm{Solution: }}}}}$

$\tt{ Perimeter \: of \: rhombus = 4a \: units}$

Here 'a' is the side.

$\tt{ Perimeter \: of \: rhombus = 56 \: cm}$

$➯ { \tt{4 \times Side = 56}} \\ </p><p></p><p>➯ \tt{Side = \dfrac{56}{4} }$

$➯ \tt{Side = 14 \: cm} \\ </p><p></p><p>\tt{Area \: of \: a \: rhombus = b \times h} \\ </p><p></p><p>➯ \tt84 = 14 \times h \\ </p><p></p><p>➯ \tt{h = \dfrac{84}{14} } \\ </p><p> </p><p> </p><p></p><p>➯ \tt{h = 6 \: cm}h=6cm$

$Height \: of \: rhombus = \orange { \underline{ \boxed{ \tt{ 6 \: cm}}}}$

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$\orange{\large{\underline{\underline{ \rm{Let's \: Verify \: It: }}}}}$

${ \boxed{ \tt{Perimeter \: of \: rhombus = 4 \times side}}}$

$➝ \tt{Perimeter = 4 \times 14 = 56 \: cm} \\ </p><p></p><p>➝ \tt{ \therefore{Perimeter \: of \: rhombus = 56 \: cm}}$

_______________________________________________

$\boxed{ \tt{Area \: of \: rhombus = b \times h}} </p><p>$

$➝ \tt{area = 14 \times 6 = 84 \: {cm}^{2} } \\ </p><p> </p><p></p><p>➝ \tt{ \therefore{area \: of \: rhombus = 84 \: {cm}^{2}}} \\ </p><p></p><p> </p><p></p><p>Hence \: Verified!!$