Question

Find the length of h. Round to the nearest hundreth.​

Answer 1

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

$\cfrac{h}{0.3}~~ = ~~\cfrac{0.4}{0.5}\implies \cfrac{h}{~~ \frac{3}{10}~~}~~ = ~~\cfrac{~~ \frac{4}{10}~~}{\frac{5}{10}}\implies \cfrac{10h}{3}~~ = ~~\cfrac{4}{5} \\\\\\ 50h=12\implies h=\cfrac{12}{50}\implies h=\cfrac{6}{25}\implies h=0.24$