A triangle has side lengths of 12 cm, 15 cm, and 20 cm. Classify it as acute, obtuse, or right.
(1 point)
Responses
acute
acute
obtuse
obtuse
right
right
There is not enough information.
To classify the triangle as acute, obtuse, or right, we can use the Pythagorean theorem. According to the theorem, if the square of the length of the longest side is equal to the sum of the squares of the other two sides, the triangle is right. If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. If the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
In this case, the longest side is 20 cm, so we will compare it to the sum of the squares of the other two sides:
12^2 + 15^2 = 144 + 225 = 369
20^2 = 400
Since 400 is equal to 369, the triangle is right. Therefore, the correct classification is: right.