$\text{Area} = \frac{1}{2}ab$
$36 = \frac{1}{2}ab$
$b = \dfrac{72}{a}$
$\dfrac{x}{a} + \dfrac{y}{b} = 1$
At C(5, 2)
$\dfrac{5}{a} + \dfrac{2}{b} = 1$
$5b + 2a = ab$
$5 \left( \dfrac{72}{a} \right) + 2a = a\left( \dfrac{72}{a} \right)$
$\dfrac{360}{a} + 2a = 72$
$360 + 2a^2 = 72a$
$a^2 - 36a + 180 = 0$
$a = 30 ~ \text{ and } 6$
$b = 2.4 ~ \text{ and } ~ 12 \text{ respectively}$
For a = 30 and b = 2.4
$L_{AB} = \sqrt{30^2 + 2.4^2} = 30.10 ~ \text{units}$
For a = 6 and b = 12
$L_{AB} = \sqrt{6^2 + 12^2} = 13.42 ~ \text{units}$
Answer = [ C ]
