By Pythagoras the long side of the triangle is 87. Since a+b is 100 we can change b to 100-a. The small triangle at the top shares an angle with the large triangle, and since both are also right-angled the two triangles are similar.
87/63 = (63-a)/(a-13)
87(a-13) = 63(63-a)
87a-1131 = 3969-63a
150a = 5100
a = 34
b = 100-a = 66
a*b = 34*66 = 2244
