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
[tex]24 + AC + 24 = 82[/tex]
Collect like terms
[tex]AC = 82 - 24 - 24\\AC = 34[/tex]
Given that, the triangle is rotated at D, the midpoint of AC
The length of the midpoint has to be calculated
[tex]D = \frac{1}{2}AC[/tex]
[tex]D = \frac{1}{2} * 34[/tex]
[tex]D = \frac{34}{2}[/tex]
[tex]D = 17[/tex]
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
