ABCD is a rhombus of side 20 cm and has two angles of 60- each- The length of the diagonal AC is-A- 10 cmB- 20 cmC- 15 cmD- None of these

The correct option is B 20 cmGiven: A rhombus with side 20 cm and a pair of opposite angle as 60^∘ Consider a rhombus ABCD Sin 30= AE/AB = AE/20 1/2=AE/20 ⇒ A ...

ABCD is a rho...

Question

ABCD is a rhombus of side 20 cm and has two angles of $60^{\circ}$ each. The length of the diagonal AC is:

10 cm

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20 cm

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15 cm

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None of these

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Solution

The correct option is B 20 cm
Given: A rhombus with side 20 cm and a pair of opposite angle as $60^{\circ}$

Consider a rhombus ABCD

$S i n 30 = \frac{A E}{A B} = \frac{A E}{20} \frac{1}{2} = \frac{A E}{20} \Rightarrow A E = 10 \Rightarrow A C = 2 A E$ [ $∵$ Diagonals of a rhombus bisect each other]
$∴ A C = 20 c m$

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The correct option is B 20 cmGiven: A rhombus with side 20 cm and a pair of opposite angle as 60∘ Consider a rhombus ABCD Sin 30=AEAB=AE2012=AE20⇒AE=10⇒AC=2AE [∵ Diagonals of a rhombus bisect each other] ∴AC=20 cm

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