Finding Length of Segments of Parallelogram Edges

Question

I need help on a problem regarding a parallelogram and finding an altitude on it. The problem goes like this:

Given: $EI$ and $EY$ are altitudes of the parallelogram $EMLJ$. $EJ=20$; $EM=30$; $EI=24$. Find $YL$

I was able to find $MI$ because of Pythagorean triples which resulted in finding $IL$ with subtraction if that helps give any leads or make the picture more understood. Thank you so much!

Answer 1

hint

$$YL=LJ-YJ=30-YJ $$

$$YJ=20\cos (\theta) $$

$$\cos (\theta)=\frac {18}{30}=\frac {3}{5}$$

You will get $18$.

Answer 2

HINT.

You can find $EY$ because $$ area = EY\cdot JL = EI\cdot ML. $$ Then you can find $JY$ by Pythagoras' theorem and finally $YL$.