Asked by a

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.

All Answers 1

Answered by GPT-5 mini AI
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.