Really simple question but I am stuck. The following information is given: $$BD=8,\quad AB = 6,\quad ED =5,\quad EF = EC$$ and we want to find $AF$.
If we have three $90^\circ$, what does that really mean, and how I can find $AF$?
Asked
Active
Viewed 168 times
3
Zev Chonoles
- 129,973
SSK
- 673
3 Answers
1
Alternative way to prove this:
Since $EF+EC=6$ and $EF=EC$, this implies that $EC=3$
Notice that triangles ABD and ECD are similar in sharing a right angle, the angle at D. There is a scaling factor of 2 as $AB=6$ and $EC=3$.
Since $BC=CD$ and $BD=8$ this implies $BC=4$ as this is half the overall distance.
$AF$ is the same length as the rectangle has opposite sides of the same length.
JB King
- 3,644
1
If you can see triangles $\widehat { AFE } $ and $\widehat { DCE } $ are the same, then everything becomes easy. Because $\widehat { AFE } $=$\widehat { AFE } $, $AF$=$CD$, because of the rectangle $AF$=$BC$, then $AF$=$BC$=$CD$. Finally $AF$=$BC$=$4$ because $BC$ is half of the $BD$. Without math you can solve the question.
newzad
- 4,855
-
Same could be misinterpreted as congruent which they aren't since the sides aren't the same length. They are similar triangles though I'd argue you did use some arithmetic to get the answer with a half of something computation here. – JB King May 19 '13 at 20:46
0
Hint: $$\begin{align*} AB=6,\;BD=8,\;\text{Pythagorean theorem}&\implies AD=\mathbin{?}\\\\ ED=5&\implies AE=\mathbin{?}\\\\ EF+EC=AB=6,\;EF=EC&\implies EF=\mathbin{?}\\\\ AE=\mathbin{?},\;EF=\mathbin{?},\;\text{Pythagorean theorem}&\implies AF=\mathbin{?}\\\\ \end{align*}$$
Zev Chonoles
- 129,973