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If two triangles are congruent then the perimeters are equal?
Yes.
Are the perimeters equal if two triangles are congruent?
Yes
Is it true that when equilateral triangles have equal perimeters they must also have equal areas?
Yes.
The sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle?
Let's denote the perimeter of the first triangle as P. Since the triangles are congruent, the perimeter of the second triangle is also P. The sum of their perimeters is then 2P. According to the given statement, this sum is three times the perimeter of the first triangle. So we have the equation 2P = 3P. Simplifying, we find that P = 0, which is not a valid solution. Therefore, there is no triangle for which the sum of the perimeters of two congruent triangles is three times the perimeter of the first triangle.
How many shapes are there with the perimeter of 32cm?
There are an infinite number of shapes with perimeters of 32.Even if you stuck to one shape and asked: "How many squares ..." or "How many circles ... " or "How many triangles ... ",there are still an infinite number of each shape that all have perimeters of 32.
