The Altitude rule- (shown on my work) When there is an altitude on the hypotenuse of a right triangle, then 3 similar triangles are formed. The altitude rule allows us to use proportions and cross-multiplication to solve for missing lengths.
(If you were asked to find the lengths of the legs of the big triangle you would have to use the leg rule instead of the altitude rule)
I used my previous work I've done for similar problems, and just fine-tuned it to fit your question and your values.
CONTINUED WORK(from the picture):
x²=9216
x=√9216
x= 96 units
Answer:
x=96 units
Sorry I changed up the colors on you on my work. I hope you still find it easy to understand. Please let me know if there is anything you are still confused about in the comments below! :)