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What is the maximum number of points common to the intersection of a s
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09 Jun 2021, 07:13
09 Jun 2021, 07:13
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What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Re: What is the maximum number of points common to the intersection of a s
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09 Jun 2021, 07:20
09 Jun 2021, 07:20
1
This is not a difficult question.
Try drawing a square and a triangle on the square such in the image below. Thus a triangle and a square can intersect at atmost six side.
https://encrypted-tbn0.gstatic.com/imag ... A&usqp=CAU
Hope this helps
Posted from my mobile device
Try drawing a square and a triangle on the square such in the image below. Thus a triangle and a square can intersect at atmost six side.
https://encrypted-tbn0.gstatic.com/imag ... A&usqp=CAU
Hope this helps
Posted from my mobile device
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Joined: 10 Apr 2015
Posts: 6218
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Re: What is the maximum number of points common to the intersection of a s
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09 Jun 2021, 07:32
09 Jun 2021, 07:32
Carcass wrote:
What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
We might start by examining the number of ways that ONE SIDE of a triangle can intersect a square.
In other words, in how many ways can a LINE intersect a square?
After a bit of mental imagery, we might conclude that a SINGLE LINE can intersect a square in at MOST 2 ways
A triangle is composed of THREE LINE SEGMENTS.
If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line)
So, the correct answer must be 6 or less
At that point, if we're able to sketch a scenario in which there are 6 intersections, we can be certain that this is, indeed, the GREATEST number of intersections.
Answer: C
Cheers,
Brent
