# Integer-sided isosceles triangle with area equal to $120$

BdMO National 2013 Junior Q. 2:

Two isosceles triangles are possible with 120 square unit area of each and length of edges are integers. Such one is with 17, 17 and 16 unit edges. Determine the length of edges of second one. [Hint: In $\bigtriangleup ABC$ if $AB = AC$ and $AD$ is perpendicular to $BC$ then $BD = CD$ .]

• Sketch $\triangle ABC$. As mentioned in the hint, the altitude $AD$ bisects the triangle into equal halves, in fact with integer sides. Rearrange these two pieces. Better to draw and figure out, verbal description is perhaps more complex than drawing. – Macavity Feb 8 '14 at 8:52
So, the answer is $30,17,17$.