Answer:
B and C
Explanation:
We can determine which three sides will form a right triangle using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
- a and b are the legs,
- and c is the hypotenuse and the longest sides
- Thus, a three side lengths can only form a right triangle if the sum of the squares of the shorter sides equal the square of the longest side (the hypotenuse)
- We can simply check A, B, and C to see which side lengths form a right triangle:
A:
- 5 and √8 (approximately 2.236) are the shorter sides, so we plug these in for a and b in the Pythagorean theorem;
- 33 is the longest side, so we plug it in for c:
5^2 + (√8)^2 = 33^2
25 + 8 = 1089
33 ≠ 1089
Because 33 is not equal to 1089, these three lengths do not form a right triangle.
B:
- 8 and 15 are the shorter sides, so we plug these in for a and b in the Pythagorean theorem;
- 17 is the longest side, so we plug it in for c:
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Thus, these three side lengths form a right triangle.
C:
- The two √2 (approximately 1.414) are the shorter sides, we plug these in for a and b in the Pythagorean theorem;
- 2 is the longest side, so we plug it in for c:
(√2)^2 + (√2)^2 = 2^2
2 + 2 = 4
4 = 4
Thus, these three side lengths also form a right triangle.