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Compare the square of the largest side length to the sum of the squares of the other two side lengths.
Is a triangle? Yes
Classification: Obtuse
Explanation: See solution.
We want to determine whether the given side lengths can be the measures of a triangle. To do so, we will use the following theorem.
Triangle Inequality Theorem |
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
4+12 ? > 14 | 14+4 ? > 12 | 12+14 ? > 4 |
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16 > 14 | 18 > 12 | 26 > 4 |
Therefore, these sides lengths can indeed form a triangle. Now, we want to determine whether the triangle formed by the given side lengths is acute, right, or obtuse. To do so, we will compare the square of the largest side length to the sum of the squares of the other two side lengths. Let a, b, and c be the lengths of the sides, with c being the longest.
Condition | Type of Triangle |
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a^2+b^2 < c^2 | Obtuse triangle |
a^2+b^2 = c^2 | Right triangle |
a^2+b^2 > c^2 | Acute triangle |