Question

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​

Answer 1

A.) 0.9cm, 1.2cm, 1.5cm

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)

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Comment on 3:4:5

This 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.