A triangle has side lengths of 11 cm, 19 cm, and 28 cm. Classify it as acute, obtuse, right, or not a triangle
In order to determine the classification (acute, obtuse, right, or not a triangle) of the triangle with side lengths 11 cm, 19 cm, and 28 cm, we can apply the Pythagorean theorem.
Let's start by finding the square of the longest side (28 cm): 28^2 = 784.
Next, we determine the sum of the squares of the other two sides: 11^2 + 19^2 = 121 + 361 = 482.
Now, we can analyze the values we obtained. If the square of the longest side is equal to the sum of the squares of the other two sides, we have a right triangle. If the square of the longest side is greater than the sum of the squares of the other two sides, we have an obtuse triangle. However, if the square of the longest side is less than the sum of the squares of the other two sides, we do not have a triangle.
In this case, 784 is greater than 482, meaning the triangle is an obtuse triangle.