Answer:
BD = 8
Explanation:
To solve this, you need to use Pythagorean theorem which states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
For △ABC, AC (4+16) is the hypotenuse
=> AC^2 = AB^2 + BC^2
For △ABD, AB is the hypotenuse
=> AB^2 = AD^2 + BD^2
For △BCD, BC is the hypotenuse
=> BC^2 = BD^2 + CD^2
Therefore
AC^2 = AB^2 + BC^2
AC^2 = (AD^2 + BD^2) + (BD^2 + CD^2)
20^2 = 4^2 + BD^2 + BD^2 + 16^2
400 - 16 - 256 = 2BD^2
BD^2 = 128/2 = 64
BD = √64 = 8