Use the pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle. check all that apply.
a. 3, 4, 5
b. 4, 11, 14
c. 9, 14, 17
d. 8, 14, 16
e. 8, 15, 17

The Pythagorean theorem states that the square of the hypotenuse is equal to  the sum of the squares of the legs:

The hypotenuse is the side with the greatest length.

Check all options:

1. c=5, a=3, b=4:

true.

2. c=14, a=4, b=11:

false.

3. c=17, a=9, b=14:

false.

4. c=16, a=8, b=14:

false.

5. c=17, a=8, b=15:

true.

correct options are A and E.

so, converting firstly the mixed fractions to improper fractions and then "adding".