Plz ! using similarity solve for x. show all work.

We know that
see the attached figure with letters 

applying the Pythagorean theorem

in the triangle ABE
BE²=x²-9²------------> equation 1

in the triangle ABD
BD²=(16+9)²-x²--------> BD²=25²-x²-----------> equation 2

in the triangle BED
BD²=(BE)²+16²--------------> equation 3

I substitute 1 and 2 in 3
25²-x²=x²-9²+16²------> 25²+9²-16²=2x²-------> 2x²=450--------> x²=225
x=√225--------> x=15 cm

the answer is x=15 cm