Question

Urgent. Refer to the picture and Solve for x

Answer 1

Label 4 points on the largest right triangle, A, B, C, D. There is a theorem (right triangle altitude theorem or geometric mean theorem) that establishes similarity between the 3 triangles in the image.

`\Delta ABC\sim\Delta ADB`

So corresponding sides occur proportionally to one another such that

`(AC)/(AB)=(AB)/(AD)\implies\frac x9=\frac{16}x`

`\implies x^2=144\implies x=12`