Question

determine if the segment lengths form a triangle. if so, would the triangle be acute, right, or obtuse? 24, 30, 6√43 a. no, the segments do not form a triangle. b. yes, the segments would form an acute triangle. c. yes, the segments would form a right triangle. d. yes, the segments would form an obtuse triangle. please select the best answer from the choices provided a b c d

Explanation:

Step1: Identify longest side

Longest side is $6\sqrt{43}$

Step2: Check triangle inequality

Verify $24+30 > 6\sqrt{43}$: $54 > 6\sqrt{43} \implies 9 > \sqrt{43} \implies 81 > 43$, true.

Step3: Apply Pythagorean theorem

Calculate $24^2 + 30^2 = 576 + 900 = 1476$
Calculate $(6\sqrt{43})^2 = 36 \times 43 = 1476$

Step4: Classify triangle

Since $24^2 + 30^2 = (6\sqrt{43})^2$, it is a right triangle.

Answer:

C. Yes, the segments would form a right triangle.