Question

If ABCD is a rectangle, AD = 9, AC = 22, B Ж X D Find the Length of all the Segments in the Parallelogram. AD AC = CD =

Answer 1

Since we're working on a rectangle, we know that the diagonals intercect right in the middle, and that they're all equal.

This way,

$AC=BD=22$

And

$AE=BE=DE=CE=\frac{1}{2}AC=11$

Now, we also know that

$AD=BC=9$

And using the Pythagorean theorem, we have that:

$AD^2+CD^2=AC^2$

Solving for CD,

$\begin{gathered} CD=\sqrt[]{AC^2-AD^2} \\ \rightarrow CD=20.07 \end{gathered}$

And we know that:

$AB=DC=20.07$

This way, the final answers would be:

$\begin{gathered} AD=9 \\ AC=22 \\ CD=20.07 \\ AB=20.07 \\ BD=22 \\ BC=9 \\ AE=11 \\ BE=11 \\ CE=11 \\ DE=11 \end{gathered}$