Question

A triangle has sides lengths of 9 cm, 12 cm, and 15 cm.

Determine whether this is a right triangle and why.

Answer 1

Explanation:

Yes bc 9^2+12^2=15^2

Answer 2

• Yes it is a right triangle
• The side lengths satisfy the Pythagorean theorem equation

Explanation:

We can test these numbers to see if they satisfy the Pythagorean theorem equation:

15² = 9² + 12²

225 = 81 + 144 . . . . true

Since the numbers satisy the Pythagorean theorem relation, they belong to a right triangle.

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You can recognize that the ratio of side lengths is ...

9 : 12 : 15 = 3 : 4 : 5

Further, you can recognize that the side lengths 3, 4, 5 belong to the right triangle with the smallest integer side lengths that satisfy the Pythagorean theorem. Hence the 9 : 12 : 15 triangle is similar (by a scale factor of 3) to a right triangle, thus is a right triangle.