The square of each internal angle bisector of an integer triangle is rational, because the general triangle formula for the internal angle bisector of angle " A " is \ tfrac { 2 \ sqrt { bcs ( s-a ) } } { b + c } where " s " is the semiperimeter ( and likewise for the other angles'bisectors ).
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For an isosceles triangle with equal sides of length " a " and base of length " b ", the general triangle formulas for ( 1 ) the length of the triangle-interior portion of the angle bisector of the vertex angle, ( 2 ) the length of the median drawn to the base, ( 3 ) length of the altitude drawn to the base, and ( 4 ) the length of the triangle-interior portion of the perpendicular bisector of the base all simplify to \ tfrac { 1 } { 2 } \ sqrt { 4a ^ 2-b ^ 2 }.
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