Answer:
The length of AC = 25
Step-by-step explanation:
Triangle ABD is a right triangle and can use the Pythagorean theorem which is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
one leg is BD = a = 12
hypothenuse is BA = c = 15
other leg is AD = b, which we need to find
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]b^{2}[/tex] = [tex]c^{2}[/tex] - [tex]a^{2}[/tex]
[tex]b^{2}[/tex] = [tex]15^{2}[/tex] - [tex]12^{2}[/tex]
[tex]b^{2}[/tex] = 225 - 144
[tex]b^{2}[/tex] = 81
b = leg AD = 9
The length of AC = AD + 16 (given in picture) = 9 + 16 = 25
I hope this helps
