The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.
2 answers:
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
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, <em>A cone with base radius of 17 in</em>
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According to the question of the statement, we can conclude that
PQ = 2B
QR = 2B
PR = base = B
Perimeter = P = 105
P = PQ + QR + PR
105 = 2B + 2B + B
B = 21
<h2>PQ = 2B = 42</h2><h2>QR = 2B = 42</h2>