# A triangle has area #Delta# ... ?

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The scalene triangle of area #Delta# has lengths #a , b # and #c # such that #a in QQ# and #b^n , c^n notin QQ , AA n in ZZ # Does there exist values of #a , b # and #c# such that #Delta^(2m+1) in QQ # for some #m in ZZ^+#

If not, give a proof

The scalene triangle of area

If not, give a proof

##### 1 Answer

Here's a right triangle that does the trick:

#### Explanation:

I'll assume we get to exclude

Let's see if we can do it with a right triangle

Let's pick

That's a solution. We have