If the straight lines y = 4 - 3x, ay = x + 10, and 2y + bx + 9 = 0 represent three consecutive sides of a rectangle then ab =

$2\mathrm{y}+\mathrm{bx}+9=0$

$\Rightarrow \mathrm{y}=\left(-\frac{\mathrm{b}}{2}\right)\mathrm{x}+\left(-\frac{9}{2}\right)$                 …… (1)

$\mathrm{y}=-3\mathrm{x}+4$

$\Rightarrow \mathrm{y}=(-3)\mathrm{x}+4$                  ……. (2)

$\mathrm{ay}=\mathrm{x}+10$

$\Rightarrow \mathrm{y}=\left(\frac{1}{\mathrm{a}}\right)\mathrm{x}+\left(\frac{10}{\mathrm{a}}\right)$        ……. (3)

Let (1), (2) be opposite sides of a rectangle so slopes are equal

$\therefore -\frac{\mathrm{b}}{2}=-3\Rightarrow \mathrm{b}=6$

(2) and (3) are adjacent sides then product of slopes=-1

$\therefore (-3)\left(\frac{1}{\mathrm{a}}\right)=-1\Rightarrow \mathrm{a}=3$.

Therefore ab = 18.