Question

Which triangles are similar to AED? The length of segment EF aid 8 units and the length of segment ED aid 10 units I have to find the length of segment FA. What is the length of segment FA is __ units?

Answer 1

`FA=10.67\: or\: 10(2)/(3)\: \text{units}`

1) In this question, we can see a right triangle ΔAED. So, based on Similarity we can write the following relations useful to help us out finding the length FA.

2) So, Let's begin finding the length of FD, using the Pythagorean Theorem considering the right triangle ΔEFD

`\begin{gathered} a^2=b^2+c^2 \\ 10^2=8^2+c^2 \\ 100=64+c^2 \\ 100-64=c^2 \\ \sqrt[]{c^2}^{}=\sqrt[]{36} \\ c=\pm6 \end{gathered}`

Since there are no negative dimensions, let's consider just the positive value: FD=6

2.2) We can derive the following formula applying similarity once more and write:

`\begin{gathered} EF^2=FA\cdot FD \\ 8^2=FA\cdot6 \\ FA=(64)/(6)=(32)/(3) \\ FA\approx10.67 \end{gathered}`

Thus this is the answer