Isosceles triangles with a given side and area

An isosceles triangle has two equal sides of length \(13\) cm and an area of \(60\text{ cm}^2\). Its height from the apex to the base is \(h\) cm and half of its base is \(b\) cm.

1. Show that \(b^2+h^2=169\) and \(bh=60\).[2]
2. Find the values of \((b+h)^2\) and \((b-h)^2\).[3]
3. Hence find all possible lengths of the base of the triangle.[2]