Question

The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.

Answer 1

Answer:

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

$24 + AC + 24 = 82$

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

$D = \frac{1}{2}AC$

$D = \frac{1}{2} * 34$

$D = \frac{34}{2}$

$D = 17$

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

Answer 2

Answer:

A

Step-by-step explanation: