Question

If the diagonal of a rhombus are 18cm and 24cm respective ,then its side is equal to?​

Answer 1

Answer:-

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Given:

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▪︎Diagonal ¹ of rhombus = 18cm

▪︎Diagonal ² of rhombus = 24 cm

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To Find:

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▪︎Side of rhombus

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Solution:

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Let the rhombus be ABCD with diagonals AC and BD bisects each other at O.

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As, Diagonal bisect each other;

AO = ½ × AC = 9cm

BO = ½ × BD = 12cm

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In ∆ AOB

AO = 9cm

BO = 12 cm

∠AOB = 90° [Bisecting each other at 90°]

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As, ∆ AOB is a right angle triangle

By pythagorean theorem

(AB)² = (AO)² + (BO)²

$\sf{}\implies AB = \sqrt{(9)² + (12)²}$

$\sf{}\implies AB = \sqrt{81 + 144}$

$\sf{}\implies AB = \sqrt{225}$

$\sf{}\implies AB = \sqrt{15 × 15}$

$\boxed{\pink{\sf{\therefore AB = 15cm}}}$

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As, it is a rhombus it's all sides are equal.

AB = BC = CD = DA = 15cm

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$\boxed{\purple{\bf{Hence,\ each\ side\ of\ rhombus\ is\ 15cm.}}}$

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Properties of rhombus:-

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▪︎All sides are equals.

▪︎Diagonal are unequals.

▪︎Diagonals bisect each other equally.

▪︎Diagonal bisect each other at 90°.