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.

A cone with base radius of 17 in

Step-by-step explanation:

Given

Triangle ABC

Where

AB = BC = 24in

D = Midpoint of AC

Required

Which best describes the resulting three-dimensional figure?

First, the length of the third side of the triangle has to be calculated

The sides of triangle ABC are AB, AC and BC

Given that the perimeter = 82 in

AB + AC + BC = 82

Recall that AB = BC = 24in; The equation becomes

Collect like terms

Given that, the triangle is rotated at D, the midpoint of AC

The length of the midpoint has to be calculated

At this point, we can dismiss options C and D.

This is because; a triangular pyramid is formed by more than 1 triangles (at least 3 triangle) and in this case, we're dealing with only 1 triangle.

So, we have option A and B to select from.

When the triangle is rotated at point D, it generates a cone such that the radius of the cone is the distance at point D.

This implies that, a cone with base radius D is generated.

Recall that D = 17.

Hence, A cone with base radius of 17 in

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