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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Two figures are similar if one is the scaled version of the other.
This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.
To be more precise, you only need two steps to prove that every two circles are similar:
- Translate one of the two circles so that they have the same center
- Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well
Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.
Recapping, we have:
- Start with circle X and radius r
- Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
- Scale the radius of circle X' until it becomes
. This new circle, say X'', is similar to X' because you only scaled it
So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.