She got the answers by using the Pythagorean Theorem, a^2 + b^2 = c^2.
to find AB:
1^2 + 3^2 = c ^2
1 + 9 = c^2
10 = c^2
_/10 = _/c^2
3.16 = c
so AB equal 3.16
to find BC:
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
_/25 = _/c^2
5 = c
so BC equals 5
CD has the same lengths as BC, so the problem is the exact same, making the answer 5 as well.
AD has the same lengths as AB, so the problem is the exact same, making the answer 3.16 as well.