Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?

An equilateral has three equal sides. You can have two squares on each side: AB, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. You can also have two squares on each side - BC, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. Again, you can have two squares on each side - CA, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC. In addition, AB, BC and CA can be a diagonal of squares.

TL;DR

In conclusion, you have 9 squares in all - 3 as diagonals of squares and 6 as sides of squares. Brainliest appreciated!

Athenalsun Athenalsun · Answer 2 · 2021-01-23T23:56:50+01:00

Athenalsun Athenalsun

23-01-2021

No square shares more than two vertices with the equilateral triangle, so we can find the number of squares having two of their vertices at two given points and triple the result. Given 2 points, 3 squares may be drawn having these points as vertices. The figure below shows a red equilateral triangle with the 3 squares that correspond to one of the sides of the triangle. Therefore, 9 squares share two vertices with the equilateral triangle.

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