Question

If BC -16 and BD-9 then find the length of BA. Show the work you use to find your answer. Draw the two similar triangles separately to help set up the proportion.

Answer 1

In right triangle the leg is geometrical mean of its projection on the hypotenuse and the hypotenuse. Thus,

`AB^2=BD\cdot BC`.

Substitude BC=16, BD=9, then

`AB^2=9\cdot 16,\\ AB^2=144,\\ AB=12`.

Answer: AB=12