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Question

# A rhombus whose side measures 40 cm has one of its angles as 60∘,, then the length of its diagonals are

A

40 cm, 80 cm

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B

40 cm, 403 cm

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C

403 cm, 80 cm

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D

80 cm, 803 cm

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Solution

## The correct option is B 40 cm, 40√3 cm Let ABCD be the given rhombus with AB=AD=40 cm and ∠ A=60∘ ∠ CAB=CAD=30∘ (Diagonal of a rhombus bisects the angle) In Δ AOB ∠ AOB=90∘, (diagonal bisect each other at 90∘) ∠ OAB=30∘, ∠ OBA=60∘ Hence, angle of triangle AOB are 30∘, 60∘, 90∘ So, the corresponding sides can be calculated as ⇒sin(30):sin(60):sin(90) ⇒12:√32:1 ⇒1:√3:2 30∘60∘90∘x:x√3:2x↓↓↓OBOAAB↓↓↓20 cm20√3 cm40 cm OA=20√3, hence AC=40√3 cm (O is midpoint of AC as diagonals of a rhombus bisect each other) Similarly OB=20 cm, hence BD=40 cm

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