math problem?

Question

there is a right angle triangle
A to C is 15
A to B is 20
and a line going through the middle of the triangle from A to D is 17
what is the length of DB?

Answer 1

A diagram would really help...but I'll assume that you mean that:

AC is the base of the triangle
AB is the hypotenuse of the larger triangle
AD is the hypotenuse of a smaller triangle inside the larger triangle

If so, then to find DB, we need to find the missing side of both triangles and subtract the smaller from the larger.

Large side:

15² + x² = 20²
225 + x² = 400
x² = 400 - 225 = 175
x = √175 = √(25(7)) = 5√7

Small side:

15² + x² = 17²
225 + x² = 289
x² = 289 - 225 = 64
x = √64 = 8

So the length DB would be given by:

5√7 - 8