which of the following could be side lenths of a right triangle? A.) 0.9cm, 1.2cm, 1.5cm B.) 0.9cm, 1.5 cm, 1.5cm C.) 0.9 cm, 1.2cm, 1.8cm D.) 0.9cm, 0.6cm, 1.5cm
Accepted Solution
A:
Answer: A.) 0.9cm, 1.2cm, 1.5cmStep-by-step explanation:The side ratios of the offered answers are ... A — 3:4:5 . . . . . . obviously a right triangle B — 3:5:5 . . . . . . isosceles, but not a right triangle C — 3:4:6 . . . . . . an obtuse triangle D — 3:2:5 . . . . . . not even a triangle (just a line segment)_____Comment on 3:4:5This set of small integers appears often in problems involving right triangles. It is the smallest "Pythagorean triple" — a set of integers that satisfies the relationship of the Pythagorean theorem — and it is the only Pythagorean triple that is an arithmetic sequence (differences between the numbers are the same).When you see a triangle with sides in these ratios, you know it is a right triangle. When you see a right triangle with two of the sides having a ratio of 3:4, 3:5, or 4:5 (where "5" is the hypotenuse), then you know the length of the remaining side.