Question

See attachment.

Answer 1

Find AC and BD

Answer 2

Triangle BCD is a right triangle.
The Pythagorean Theorem says √35 ^2 = 5^2 + x^2 where x = BD.

35 = 25 + x^2
10 = x^2
√10 = x = BD

Answer 3

Look at right triangle BCA

Segment BD is the altitude drawn to the hypotenuse.

If the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

So CD is to BD as BD is to DA

5/ √10 = √10/ DA

5 DA = 10

DA = 2

Because AC = CD + DA, then AC = 5 + DA = 5 + 2 = 7.