Tagged Questions
18
votes
4answers
104 views
Ways to fill a $n\times n$ square with $1\times 1$ squares and $1\times 2$ rectangles
I came up with this question when I'm actually starring at the wall of my dorm hall. I'm not sure if I'm asking it correctly, but that's what I roughly have:
So, how many ways (pattern) that there ...
58
votes
4answers
1k views
Probability that a stick randomly broken in five places can form a tetrahedron
Randomly break a stick in five places.
Question: What is the probability that the resulting six pieces can form a tetrahedron?
Clearly satisfying the triangle inequality on each face is a necessary ...
0
votes
0answers
95 views
geometry, problem solving!
A friend gave me this problem but I have no idea how to approach it.
Suppose you are given a triangle $ABC$. Pick points $P$ inside or on perimeter, such that the perimeter of the triangle ...
1
vote
3answers
91 views
How to find the best point?
I want to find x in the figure below where it must be as close as possible to 0, but not near to red points (the minimum distance of x to each red point must be at least 1).
1
vote
1answer
173 views
Maximum area for fixed perimeter of a triangle
I'm trying to prove that the triangle of largest area for a given perimeter is equilateral, but I'm having some difficulties.
I've done 2 different proofs for a similar problem but for rectangles - ...
4
votes
2answers
231 views
Folding a rectangular paper sheet
You are given a rectangular paper sheet. The diagonal vertices of the sheet are brought together and folded so that a line (mark) is formed on the sheet. If this mark length is same as the length of ...
5
votes
2answers
70 views
Help with a geometry problem
The problem says:
A triangle has its lengths in an arithmetic progression,
with difference d. The area of the triangle is t. Find the dimensions.
the solution says:
the notation can be even better if ...
13
votes
2answers
389 views
The Farmyard problem
Problem:
There is a farmer who has a $1\text{ mile}\times 1\text{ mile}$ square piece of land. He knows that there is a completely straight pipe underneath some part of his property, but it could ...
-1
votes
2answers
357 views
In △ ABC, D is the midpoint of AB, while E lies on BC satisfying BE = 2EC. If m∠ADC=m∠BAE, what is the measure of ∠BAC in degrees?
In △ABC, D is the midpoint of AB, while E lies on BC satisfying BE = 2EC. If m∠ADC=m∠BAE, what is the measure of ∠BAC in degrees? I know already that angle A and angle D are congruent because ...
