Question

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.

Answer 1

A

Explanation:

Answer 2

A cone with base radius of 17 in

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

`24 + AC + 24 = 82`

Collect like terms

`AC = 82 - 24 - 24\\AC = 34`

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

The length of the midpoint has to be calculated

`D = (1)/(2)AC`

`D = (1)/(2) * 34`

`D = (34)/(2)`

`D = 17`

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