Question

The area of a rhombus is 225 sq cm. if the length of one of its diagonals is 15 cm, find the length of other diagonal ​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Area of a rhombus is 225 sq. cm

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• Length of one diagonal = 15 cm

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• The length of other diagonal

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the length of other diagonal be "x"

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

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➠ $\sf \dfrac { Diagonal \ 1 \times Diagonal \ 2 } { 2 }$ -----(1)

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• Area = 225 sq. cm

• Diagonal 1 = 15 cm

• Diagonal 2 = x

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$\underline{\bold{\texttt{Putting these values in (1) }}}$

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➠ $\sf Area = \dfrac { Diagonal \ 1 \times Diagonal \ 2 } { 2 }$

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➜ $\sf 225 = \dfrac { 15 \times x } { 2 }$

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➜ 225 × 2 = 15x

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➜ 450 = 15x

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➜ $\sf x = \dfrac { 450 } { 15 }$

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➨ x = 30 cm

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• Hence the length of other diagonal of the given Rhombus is 30 cm

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Additional information

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• Perimeter of rhombus = 4 × Side

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

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Area of a rhombus is 225 sq. cm

$\:\:$

• Length of one diagonal = 15 cm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• The length of other diagonal

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the length of other diagonal be "x"

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { Diagonal \ 1 \times Diagonal \ 2 } { 2 }$ -----(1)

$\:\:$

Area = 225 sq. cm

Diagonal 1 = 15 cm

Diagonal 2 = x

$\:\:$

$\underline{\bold{\texttt{Putting these values in (1) }}}$

$\:\:$

➠ $\sf Area = \dfrac { Diagonal \ 1 \times Diagonal \ 2 } { 2 }$

$\:\:$

➜ $\sf 225 = \dfrac { 15 \times x } { 2 }$

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➜ 225 × 2 = 15x

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➜ 450 = 15x

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➜ $\sf x = \dfrac { 450 } { 15 }$

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➨ x = 30 cm

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• Hence the length of other diagonal of the given Rhombus is 30 cm

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