AM Indices Surds and Logarithm Practice Question 1
The triangle $ABC$ is such that its area is $\frac{1}{4}\left( 12+9\sqrt{3} \right)$ cm$^{2}$, the length of $AB$ is $\left( \sqrt{3}+2 \right)$cm and angle $BAC$ is ${{60}^{\circ }}$. Without using a calculator, find
(i)
the length, in cm, of $AC$ in the form $a+b\sqrt{3}$, where $a$ and $b$ are integers,
(ii)
an expression, in cm$^{2}$, for $B{{C}^{2}}$ in the form $c+d\sqrt{3}$, where $c$ and $d$ are integers.
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