Question

(Q.E.D.)
23. ABCD is a rhombus in which ZA = 60°. Find
the ratio AC: BD.​

Answer 1

Answer:

Rhombus ABCD, => diagonals AC & BD bisect at right angles. Point of intersection is O.

& also diagonals bisect interior angles of it. So, if in right triangle AOB

tan 30° = OB/OA = 1/√3

=> OB = x & OA = √3x

=> DB = 2x

& AC = 2√3x

=> DB/AC = 2x/2√3x

=> DB/AC = 1/√3

=> Ratio of diagonal opposite to smaller 60° angle to that of diagonal opposite to greater 120° angle = 1 : √3