Mathematics
ABCD is a rhombus in which ∠A = 60°. Find the ratio AC : BD.
Rectilinear Figures
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Answer
Rhombus ABCD is shown in the figure below:
In △ABD,
⇒ AB = AD (Sides of rhombus are equal.)
⇒ ∠B = ∠D = x (let) (∵ angles opposite to equal sides are equal)
⇒ ∠A + ∠B + ∠D = 180°
⇒ 60° + x + x = 180°
⇒ 2x = 180° - 60°
⇒ 2x = 120°
⇒ x = 60°.
∴ ABD is an equilateral triangle.
So, BD = AB = AD = a (let)
Since, diagonals of rhombus bisect each other,
OB =
In right angled triangle AOB,
AB2 = AO2 + OB2
a2 = AO2 +
AO2 = a2 -
AO =
AC = 2AO =
AC : BD = .
Hence, AC : BD = .
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