Question 429495: Explain why a right equilateral triangle cannot exist.
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! Assume it does exist, then in this case, the sides a,b,c are all equal. Let c be the hypotenuse side.
But in a right angle triangle we also have the condition that a^2+b^2=c^2, but a=b=c, so let's re-write the Pythagorean relationship but let's replace b with a, since they are equal, and also c with a, once again because they are equal.
so then we have a^2 + a^2 = a^2. On the left we collect the a^2 terms, there are 2. So we have 2(a^2)=a^2. Do you see why this makes no sense? How can 2 of something be equal to 1 of something.
Equivalently, try to solve a^2 + a^2 = a^2. You will find that the only solution is a=0, and since a=b=c, b and c are also 0, which means there are no numbers a,b,c where a=b=c AND a^2+b^2=c^2(c being the hypotenuse)
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