For the length of AD. The diagram shows a right angle at point B, which means that ABD is a right-angled triangle. The sides AB and BD are the legs, and AD is the hypotenuse. We

The problem asks for the length of $AD$. The diagram shows a right angle at point $B$, which means that $\triangle ABD$ is a right-angled triangle. The sides $AB$ and $BD$ are the legs, and $AD$ is the hypotenuse. We will use the Pythagorean theorem:

$$AD^2 = AB^2 + BD^2$$

From the diagram:

• The length of leg $AB = 9\text{ cm}$.
• The length of leg $BD$ is the sum of $BC$ and $CD$.

$$BD = BC + CD$$

Given $BC = 18\text{ cm}$ and $CD = 120\text{ cm}$.

Note on inconsistency: The diagram also shows $AC = 17\text{ m}$. However, if $\triangle ABC$ is a right-angled triangle at $B$ with $AB=9\text{ cm}$ and $BC=18\text{ cm}$, then $AC$ should be $\sqrt{9^2 + 18^2} = \sqrt{81 + 324} = \sqrt{405} \approx 20.12\text{ cm}$. The given $AC = 17\text{ m} = 1700\text{ cm}$ is inconsistent with these values and the right angle at $B$. Since $AC$ is not needed to find $AD$ using $\triangle ABD$, we will proceed by ignoring the value of $AC$.

$$BD = 18\text{ cm} + 120\text{ cm}$$ $$BD = 138\text{ cm}$$