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Problem of the Week

Problem D

Different Lengths

\(\triangle ABC\) is isosceles with \(AB=AC\). All three side lengths of \(\triangle ABC\) and also altitude \(AD\) are positive integers.
If the area of \(\triangle ABC\) is 60 cm\(^2\), determine all possible perimeters of \(\triangle ABC\).

Triangle ABC has point D on side BC. Altitude AD, which makes a right angle with BC, has length h.

Note: You may use the fact that the altitude of an isosceles triangle drawn to the unequal side bisects the unequal side.