Question

the area of a rhombus is 84 cm^2 when its perimeter is 56 centimetre find the height​

Answer 1

$\pink{\large{\underline{\underline{ \rm{Given: }}}}}$

☘︎ Area of a rhombus = 84 cm²

☘︎ Perimeter of rhombus = 56 cm

$\pink{\large{\underline{\underline{ \rm{To \: Find: }}}}}$

❁ The height of rhombus.

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

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

Here 'a' is the side.

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

➯ ${ \tt{4 \times Side = 56}}$

➯ $\tt{Side = \dfrac{56}{4} }$

➯ $\tt{Side = 14 \: cm}$

$\tt{Area \: of \: a \: rhombus = b \times h}$

➯ $\tt84 = 14 \times h$

➯ $\tt{h = \dfrac{84}{14} }$

➯ $\tt{h = 6 \: cm}$

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

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

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

➝ $\tt{Perimeter = 4 \times 14 = 56 \: cm}$

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

_______________________________________________

$\boxed{ \tt{Area \: of \: rhombus = b \times h}}$

➝ $\tt{area = 14 \times 6 = 84 \: {cm}^{2} }$

➝ $\tt{ \therefore{area \: of \: rhombus = 84 \: {cm}^{2}}}$

Hence Verified!!

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