Question

How to find the length of x

Answer 1

so, as you can see from the picture below

the line coming down from the right-angle, creates 3 similar triangles
a large, a medium and a small one

the large one, is the one containing the other two smaller ones... anyhow

to get "x", you can use proportions, either from large and medium or small and large so
`\bf \cfrac{large}{medium}\qquad \cfrac{15}{12}=\cfrac{9}{x}\qquad \qquad \cfrac{small}{large}\qquad \cfrac{9}{15}=\cfrac{x}{12}`

solve for "x", either proportion will do