Question

If the area of rhombus is 48cm and its diagonal is 12cm . Find its altitude

Answer 1

i hope this will help you

Answer 2

$\underline\mathfrak{Given:-}$

• $\: \: \: \: \: Area \: \: of \: \: rhombus \: \: = \: \: {48} \: {cm}^{2}$

• $\: \: \: \: \: Diagonal \: \: = \: \: {12} \: {cm}$

$\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: find \: \: its \: \: altitude.?$

$\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: Area \: \: of \: \: a \: \: rhombus \: \: = \: \: \frac{1}{2} \: \times \: {d_1} \: \times \: {d_2}.$

$\: \: \: \: \: \leadsto {48} \: \: = \: \: \frac{1}{2} \: \times \: {12} \: \times \: {d_2}.$

$\: \: \: \: \: \leadsto {48} \: \: = \: \: {6} \: \times \: {d_2}.$

$\: \: \: \: \: \leadsto \frac{48}{6} \: \: = \: \: {d_2}.$

$\: \: \: \: \: \leadsto {d_2} \: \: = \: \: {8}.$

• $\: \: \: \: \: We \: \: know, \: \: diagonal \: \: of \: \: a \: \: rhombus \: \: \\ \: \: perpendicular \: \: and \: \: bisect \: \: each \: \: other.$

$\underline\mathfrak{According \: \: To \: \: Pythagoras \: \: Theorem:-}$

$\: \: \: \: \: \leadsto {side}^{2} \: \: = \: \: {(\frac{d_1}{2})}^{2} \: + \: {(\frac{d_2}{2})}^{2}$

$\: \: \: \: \: \leadsto {side}^{2} \: \: = \: \: {(\frac{12}{2})}^{2} \: + \: {(\frac{8}{2})}^{2}$

$\: \: \: \: \: \leadsto {side}^{2} \: \: = \: \: {({6})}^{2} \: + \: {({4})}^{2}$

$\: \: \: \: \: \leadsto {side}^{2} \: \: = \: \: {36} \: + \: {16}$

$\: \: \: \: \: \leadsto {side}^{2} \: \: = \: \: {52}$

$\: \: \: \: \: \leadsto {side} \: \: = \: \: \sqrt{52}$

$\: \: \: \: \: \leadsto {side} \: \: = \: \: {7.21} \: {cm}^{2}.$

• $\: \: \: \: \: So, \\ \: \: \: \: \: each \: \: of \: \: the \: \: rhombus \: \: \leadsto \: \: {7.21} {cm}^{2}$

$\: \: \: \: \: Altitude \: \: \leadsto \: \: Area \: \: \div \: \: Side$

$\: \: \: \: \: Altitude \: \: \leadsto \: \: {48} \: \: \div \: \: {7.21}$

$\: \: \: \: \: Altitude \: \: \leadsto \: \: {6.65}$

• $\: \: \: \: \: Hence, \\ \: \: \: \: \: \: \: \: \: \: the \: \: height \: \: of \: \: the \: \: rhombus \: \: is \: \: {6.65} \: {cm}^{2}$

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