Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?

Question

Mathematics

Layton Livingston

16 January, 18:42

Can segments with lengths of 36, 48, and 60 form a triangle? If so, would the triangle be acute, right, or obtuse?

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Answers (1)

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Gordo · Answer 1

Yes, because by the triangle inequality, a triangle can be formed from three segments of which the sum of the lengths of the two shorter ones exceed the longest segment.

Here we have 36+48=84 > 60, so the three segments form a triangle.

Since the ratio of the sides are 36 : 48 : 60 form the ratio of 3:4:5, which is exactly the ratio of a right triangle, we conclude that the triangle is a right triangle.