Answer:
10. the marked answer is correct
11. acute
Step-by-step explanation:
10. You know that side lengths of 3, 4, and 5 form a right triangle. (This is usually the very first Pythagorean triple you learn: 3² +4² = 5².) It is also the only Pythagorean triple in which the side lengths are three consecutive numbers. The next triple that uses two consecutive numbers is (5, 12, 13).
A: the numbers 4, 5, 7 cannot form a right triangle. They don't match one of the triples discussed above. 4²+5² = 41 ≠ 7²
B: if we multiply these numbers by 2 to make them integers, we get 7, 8, 9. We know from above these numbers are not a Pythagorean triple, so will not form a right triangle.
C: doubling these numbers give 3, 4, 5—a Pythagorean triple you know. This is the correct choice.
D: We know sides (3, 4, 5) form a right triangle. Then sides (3, 3, 5) cannot. If two of the sides are the same length (3, 5), the triangle will only be a right triangle if the third side is the appropriate length (4).
11. From our consideration of answer A above, we know that the longest side would have to be √41 > 6 in order for the triangle to be a right triangle. Since the longest side is too short to make a right triangle, the triangle must be an acute triangle.
