A triangle has side lengths of 11 cm, 19 cm, and 28 cm. Classify it as acute, obtuse, right, or not a triangle
A. Acute
B. Obtuse
C. Right
D. Not a triangle
To classify the triangle, we need to apply the triangle inequality theorem. This theorem states that in a triangle, the sum of the lengths of any two sides must always be greater than the length of the third side.
Let's check if this condition is satisfied for the given side lengths:
11 + 19 = 30 > 28 (satisfied)
11 + 28 = 39 > 19 (satisfied)
19 + 28 = 47 > 11 (satisfied)
Since the triangle inequality theorem is satisfied for all three combinations of side lengths, we can conclude that the given side lengths form a triangle.
Next, let's classify the triangle based on the angles:
If a^2 + b^2 = c^2, where a, b, and c are the sides of the triangle, then the triangle is right-angled.
If a^2 + b^2 > c^2, then the triangle is acute-angled.
If a^2 + b^2 < c^2, then the triangle is obtuse-angled.
Using the given side lengths, let's check the conditions:
11^2 + 19^2 = 121 + 361 = 482 > 28^2 (acute-angled)
19^2 + 28^2 = 361 + 784 = 1145 < 11^2 (not obtuse-angled)
Based on these calculations, the triangle is classified as acute-angled or simply "acute", which is option A.