SOLUTION: Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?
Algebra ->
Test
-> SOLUTION: Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?
Log On
Question 1189905: Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle? Answer by ikleyn(52814) (Show Source):
You can put this solution on YOUR website! .
Let ABC be an equilateral triangle. How many squares in the same plane as ABC
share two vertices with the triangle?
~~~~~~~~~~~~~~~~~
Since the problem says nothing about possible overlaying the squares, I will assume
that overlaying is allowed and is not an issue.
Then each side of the triangle determines three such squares:
- two squares on different sides of the side that share the side,
- plus one square which has a diagonal coinciding with the side.
ANSWER. In all, there are 3 * 3 = 9 such squares.
----------------
I answered this question assuming that squares must share their vertices with that of the triangle.
