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Question

The length of the diagonal AC of a rhombus ABCD is 20 cm and one of its angle measures 120, then the length of the other diagonal BD is


A

103 cm

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B

10 cm

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C

20 cm

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D

203 cm

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Solution

The correct option is D

203 cm


ABCD is a rhombus with AC=20 cm

A=60, B=120

Here AO=12 AC=12×20=10 cm (diagonals of a rhombus bisect each other at right angles)

AOB=90

In triangle AOB, the angles are 30, 60, 90

So, the corresponding sides can be calculated as

sin(30):sin(60):sin(90)

12:32:1

1:3:2

306090x:x3:2xBOAOAB 103 cm10 cm 203 cm

BO=103 cm

BD=2×BO

BD=2×103=203 cm


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