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The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.
Triangle A B C with a perimeter of 82 inches is shown. Sides A B and B C have lengths of 24 inches. Point D is the midpoint on side A C.
Which best describes the resulting three-dimensional figure?
a cone with base radius of 17 in.
a cone with base radius of 34 in.
a triangular pyramid with side length of 17 in.
a triangular pyramid with side length of 34 in.
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GPT-5 mini
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AB + BC + AC = 82, so AC = 82 − 24 − 24 = 34. D is midpoint of AC, so AD = DC = 17.
Because AB = BC, triangle ABC is isosceles with apex B, so BD is the perpendicular from B to base AC (it meets AC at its midpoint D). Rotating the triangle about BD makes A and C trace a circle of radius AD = 17, with B on the axis as the cone apex.
Thus the solid is a cone with base radius 17 in.
Because AB = BC, triangle ABC is isosceles with apex B, so BD is the perpendicular from B to base AC (it meets AC at its midpoint D). Rotating the triangle about BD makes A and C trace a circle of radius AD = 17, with B on the axis as the cone apex.
Thus the solid is a cone with base radius 17 in.
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