Given that ACB = (9)/(16), form an equation in x. Solve the equation in (b)(ii). Hence find the length of side AC. Hence, calculate the length of side BC.

$$\frac{x+2}{2x+3} = \frac{9}{16}$$ $$\boxed{\mathbf{\frac{x+2}{2x+3} = \frac{9}{16}}}$$

b) iii) To solve the equation from part (b)(ii):

$$32 - 27 = 18x - 16x$$ $$5 = 2x$$

$$x = \frac{5}{2}$$ $$\boxed{\mathbf{x = 2.5}}$$

b) iv) To find the length of side $AC$:
The length of side $AC$ is given by the expression $(2x+3)$ cm.

$$AC = 2\left(\frac{5}{2}\right) + 3$$ $$AC = 5 + 3$$ $$AC = 8 \text{ cm}$$ $$\boxed{\mathbf{AC = 8 \text{ cm}}}$$

b) v) To calculate the length of side $BC$:
We have a right-angled triangle $ABC$ with $\angle ABC = 90^\circ$. We know $AB = (x+2)$ cm and $AC = 8$ cm. We can use the Pythagorean theorem, $AB^2 + BC^2 = AC^2$.

$$BC^2 = AC^2 - AB^2$$ $$BC^2 = (8)^2 - \left(\frac{9}{2}\right)^2$$ $$BC^2 = 64 - \frac{81}{4}$$

$$BC^2 = \frac{256}{4} - \frac{81}{4}$$ $$BC^2 = \frac{175}{4}$$

$$BC = \sqrt{\frac{175}{4}}$$ $$BC = \frac{\sqrt{175}}{\sqrt{4}}$$ $$BC = \frac{\sqrt{25 \times 7}}{2}$$ $$BC = \frac{5\sqrt{7}}{2} \text{ cm}$$ $$\boxed{\mathbf{BC = \frac{5\sqrt{7}}{2} \text{ cm}}}$$