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A semicircle with area of xπ is marked by seven points equal
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05 Oct 2017, 20:34
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Question Stats:
36% (03:12) correct
63% (02:42) wrong based on 36 sessions
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A semicircle with area of xπ is marked by seven points equally spaced along the half arc of the semicircle, such that two of the seven points form the endpoints of the diameter. What is the probability of forming a triangle with an area less than x from the total number of triangles formed by combining two of the seven points and the center of the diameter?
Re: A semicircle with area of xπ is marked by seven points equal
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15 Oct 2017, 23:15
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Bunuel wrote:
A semicircle with area of xπ is marked by seven points equally spaced along the half arc of the semicircle, such that two of the seven points form the endpoints of the diameter. What is the probability of forming a triangle with an area less than x from the total number of triangles formed by combining two of the seven points and the center of the diameter?
Re: A semicircle with area of x is marked by seven points equal
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12 Sep 2023, 01:34
2
Hey so this is my first post so Im not really sure how this goes but basically for this question, you need to have the prior knowledge that when there is a right angle triangle the area will be the greatest than from any other degree. So when the first point on the semi circle and the 4th point make a triangle it is a right angle triangle. And so when we find the area of this we get x as the area of the triangle. (1/2*square root 2x*square root 2x as the radius is square root 2x) we can then see that for thr area of the triangle to be less than x we need it to not be a right angle triangle. As point 1 on the semi circle and point 7 cant even make a triangle, there are 5 different triangles to be made by each point out of which 1 triangle will have an area x. So the probability of a triangle being less than x is 4/5
Re: A semicircle with area of x is marked by seven points equal
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24 Dec 2024, 03:20
1
it is quite arduous task to solve this one but we can guess this particular question without any knowledge total triangle form from centre and two points are 7c2 -1(the diameter)=20 so 20 in denominator and only viable option which has factor of 20 is A