Question

Each side of a rhombus is 61 cm and one of its diagonals is 22 cm long. Find (i) the length
of the other diagonal and (ii) the area of the rhombus.
plZz tell me I have ask this question second time ​

Answer 1

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

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$\large\underline{\green{\bf Given :-}}$

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• Each side of a rhombus is 61 cm

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• One diagonals is 22 cm long

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$\large\underline{\red{\bf To \: Find :-}}$

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• The length of the other diagonal

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• The area of the rhombus

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

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• Let ABCD is be a rhombus in which AB = BC = CD = DA = 61 cm

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Diagonal AC = 22 cm

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In a rhombus, diagonals bisect each other at right angles

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Therefore, AO = 11 cm

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In ∆ AOD,

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By pythagoras theorem

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➠ AD² = AO² + OD²

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➜ 61² = 11² + OD²

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➜ 3721 = 121 + OD²

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➜ 3721 - 121 = OD²

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➜ 3600 = OD²

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➜ OD = 60

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∴ BD = 2 × OD

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➜ 2 × 15

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➨ 120 cm

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• Hence the other diagonal is 120 cm

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

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➠ ½ × d1 × d2

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Where ,

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• d1 = 1st Diagonal

• d2 = 2nd Diagonal

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➜ ½ × 22 × 120

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➨ 1320 sq. cm

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