Answer:
1st problem: AC = 13
2nd problem: AC = 5
Step-by-step explanation:
First problem:
BD = DC = (1/2)BC
(1/2)BC = (1/2)10 = 5
DC = 5; AD = 12
Now we use the Pythagorean Theorem.
a^2 + b^2 = c^2
AD^2 + DC^2 = AC^2
12^2 + 5^2 = AC^2
144 + 25 = AC^2
169 = AC^2
AC = 13
Second problem:
We use the Pythagorean Theorem.
a^2 + b^2 = c^2
AB^2 + BC^2 = AC^2
4^2 + 3^2 = AC^2
16 + 9 = AC^2
25 = AC^2
AC = 5
