SOLUTION: The perimeter of an isosceles right triangle can never be a whole number. is that true? Explain.

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Question 430037: The perimeter of an isosceles right triangle can never be a whole number. is that true? Explain.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
No. Consider the (perimeter) function p%28x%29+=+2x+%2B+x%2Asqrt%282%29 where x is the length of a leg. This is equivalent to p%28x%29+=+x%282+%2B+sqrt%282%29%29 which is linear. The linear function is defined on all positive real numbers, and its range is all real numbers, including integers. Hence, it is possible for the perimeter to be an integer (for example, replace x+=+1%2F%282+%2B+sqrt%282%29%29 and you will find that the perimeter is 1).