Question

Will the lengths 36 48 and 60 centimeters form a right triangle ?

Answer 1

Yes they would form a right triangle 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

Answer 2

yes

Explanation:

These lengths are in the ratio 3 : 4 : 5, so will form a right triangle. (You are familiar with a 3-4-5 right triangle, of course.)

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If you want to check, you can see if these numbers satisfy the Pythagorean theorem:

36² + 48² = 60²

1296 + 2304 = 3600 . . . . . true

The given lengths satisfy the Pythagorean theorem, so will form a right triangle.