SOLUTION: explanation of why an isosceles right triangles perimeter cannot be a whole number?

Question 447811: explanation of why an isosceles right triangles perimeter cannot be a whole number?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
That statement is not true; it is possible for the perimeter of an isosceles triangle to be a whole number.

Suppose the sides are

, and

, where x is any positive number. The perimeter is therefore

.

Suppose

. If we assume such a value of x, then the perimeter would be

, which is an integer. In fact, we can replace the 5 in the numerator of x with any integer to obtain an integer perimeter.

However, if the side length itself was an integer, then it would be impossible. Proving this simply relies on the fact that

is irrational and cannot be multiplied by any rational number to obtain a rational number.
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