Right triangle s1milarities

Question

The question states: Each pair of triangles is similar. Find the Perimeter of the given Triangle

Answer 1

Rotate and separate the triangles to better visualize the similarities:

Then you can set up proportional ratios:

AD/BD = BD/CD

3/BD = BD/10

BD² = 30 (cross multiplying)

BD = √30

Answer 2

BD = geometric mean between AD and CD = sqrt(3*10) = sqrt(30)