Question

△ace ~ △hge. drag the correct value onto the image to fill in the lengths of ae and ca. note: not drawn to scale. drag & drop the answer. note: use ctrl+d to drag the option via keyboard.

Explanation:

Step1: Find the scale - factor

Since $\triangle ACE\sim\triangle HGE$, the ratio of corresponding sides is the same. Let the scale - factor be $k$. We know that $\frac{CE}{GE}=\frac{9}{3}=3$.

Step2: Find the length of $AE$

Corresponding to side $HE = 6$ in $\triangle HGE$, side $AE$ in $\triangle ACE$. Using the scale - factor, $AE=k\times HE$. So $AE = 3\times6=18$.

Step3: Find the length of $CA$

Corresponding to side $HG = 4$ in $\triangle HGE$, side $CA$ in $\triangle ACE$. Using the scale - factor, $CA=k\times HG$. So $CA = 3\times4 = 12$.

Answer:

$AE = 18$, $CA = 12$