Denote AB = a, then SABC=a2√34;AD=DB=a√2SABC=a234;AD=DB=a2

⇒SABD=a24⇒SACBD=a2(√3−1)4⇒SABD=a24⇒SACBD=a2(3−1)4

The answer is : √3−1≈0.73

Denote AB = a, then \(S_{ABC}=\dfrac{a^2\sqrt{3}}{4};AD=DB=\dfrac{a}{\sqrt{2}}\)

\(\Rightarrow S_{ABD}=\dfrac{a^2}{4}\Rightarrow S_{ACBD}=\dfrac{a^2\left(\sqrt{3}-1\right)}{4}\)

The answer is : \(\sqrt{3}-1\approx0.73\)