Question

△abc ~ △edc. drag the correct value onto the image to fill in the lengths of ab and ce. note: not drawn to scale. drag & drop the answer 20 5 6 9 note: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Use property of similar triangles

Since $\triangle ABC\sim\triangle EDC$, the ratios of corresponding sides are equal. That is $\frac{AB}{ED}=\frac{AC}{EC}=\frac{BC}{DC}$.

Step2: Find the ratio of corresponding sides

We know that $\frac{AC}{EC}=\frac{10}{EC}=\frac{BC}{DC}=\frac{8}{4} = 2$. So, $EC=\frac{10}{2}=5$.

Step3: Find length of AB

Also, $\frac{AB}{ED}=\frac{AB}{3}=2$. Then $AB = 2\times3=6$.

Answer:

AB = 6, CE = 5