Question

The area of a rhombus is 45 sq.cm
If one its deagonals (di) is 10 sq.cm find the other​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The area of a rhombus is 45 sq.cm

• One diagonal of the rhombus is 10 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The other diagonal

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We know that ,

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$\underline{ \underline{\bold{\texttt{Area of rhombus :}}}}$

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➠ $\sf A = \dfrac { 1 } { 2 } \times D1 \times D2$ ⚊⚊⚊⚊ ⓵

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Where ,

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• A = Area of rhombus

• D1 = First diagonal

• D2 = Second diagonal

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$\underline{ \underline{\bold{\texttt{Area of the given rhombus :}}}}$

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• A = 45 sq. cm.

• D1 = 10 cm

• D2 = D2

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⟮ Putting the above values in ⓵ ⟯

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: ➜ $\sf A = \dfrac { 1 } { 2 } \times D1 \times D2$

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: ➜ $\sf 45 = \dfrac { 1 } { 2 } \times 10 \times D2$

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: ➜ $\sf 45 = 5 \times D2$

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: ➜ $\sf D2 = \dfrac { 45 } { 5 }$

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: : ➨ D2 = 9 cm

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• Hence the other diagonal of the rhombus is 9 cm

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Additional information

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Perimeter of rhombus

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• 4a

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Where ,

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➻ a = Side of rhombus

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Properties of rhombus

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• All sides of the rhombus are equal

• The opposite sides of a rhombus are parallel

• Opposite angles of a rhombus are equal

• In a rhombus, diagonals bisect each other at right angles

• Diagonals bisect the angles of a rhombus

• The sum of two adjacent angles is equal to 180 degrees

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• The area of a rhombus is 45 sq.cm

• One diagonal of the rhombus is 10 cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The other diagonal

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of rhombus :}}}}$

$\:\:$

➠ $\sf A = \dfrac { 1 } { 2 } \times D1 \times D2$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

A = Area of rhombus

D1 = First diagonal

D2 = Second diagonal

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of the given rhombus :}}}}$

$\:\:$

A = 45 sq. cm.

D1 = 10 cm

D2 = D2

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ $\sf A = \dfrac { 1 } { 2 } \times D1 \times D2$

$\:\:$

: ➜ $\sf 45 = \dfrac { 1 } { 2 } \times 10 \times D2$

$\:\:$

: ➜ $\sf 45 = 5 \times D2$

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: ➜ $\sf D2 = \dfrac { 45 } { 5 }$

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: : ➨ D2 = 9 cm

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• Hence the other diagonal of the rhombus is 9 cm

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