1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

10 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

20 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

203 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 20√3 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 30∘60∘90∘x:x√3:2x↓↓↓BOAOAB↓↓↓ 10√3 cm10 cm 20√3 cm BO=10√3 cm BD=2×BO BD=2×10√3=20√3 cm

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Ratio of Sides of aTriangle determined using its Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program