Final answer:
A triangle with side lengths 12, 13, and 23–√ is an acute triangle.
Step-by-step explanation:
A triangle with side lengths 12, 13, and 23–√ can be determined to be an acute triangle.
To determine this, we can use the Pythagorean theorem which states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. If the equation holds true, the triangle is right; if the equation is less than, the triangle is acute; and if the equation is greater than, the triangle is obtuse. In this case, 12^2 + 13^2 is less than (23–√)^2, indicating the triangle is acute.
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