A search for all Pythagorean triples with integer sides less than 100 finds 50 such triangles.

Further search shows 2 solutions:

([9, 12, 15], [15, 20, 25], [25, 60, 65], [65, 72, 97])

([9, 12, 15], [15, 36, 39], [39, 52, 65], [65, 72, 97])

For each solution, the the shortest and the longest sides that Rob drew are {9, 97}.

Program output:

[[3, 4, 5], [5, 12, 13], [6, 8, 10], [7, 24, 25], [8, 15, 17], [9, 12, 15], [9, 40, 41], [10, 24, 26], [11, 60, 61], [12, 16, 20], [12, 35, 37], [13, 84, 85], [14, 48, 50], [15, 20, 25], [15, 36, 39], [16, 30, 34], [16, 63, 65], [18, 24, 30], [18, 80, 82], [20, 21, 29], [20, 48, 52], [21, 28, 35], [21, 72, 75], [24, 32, 40], [24, 45, 51], [24, 70, 74], [25, 60, 65], [27, 36, 45], [28, 45, 53], [30, 40, 50], [30, 72, 78], [32, 60, 68], [33, 44, 55], [33, 56, 65], [35, 84, 91], [36, 48, 60], [36, 77, 85], [39, 52, 65], [39, 80, 89], [40, 42, 58], [40, 75, 85], [42, 56, 70], [45, 60, 75], [48, 55, 73], [48, 64, 80], [51, 68, 85], [54, 72, 90], [57, 76, 95], [60, 63, 87], [65, 72, 97]]

50

([9, 12, 15], [15, 20, 25], [25, 60, 65], [65, 72, 97])

([9, 12, 15], [15, 36, 39], [39, 52, 65], [65, 72, 97])

-----------------------

triangles = []

for a in range(1,100):

    for b in range(a,100):

        left = a**2 + b**2

        for c in range(b,100):

            if c**2 == left:

                pythag_triple = sorted([a,b,c])

                if pythag_triple not in triangles:

                    triangles.append(pythag_triple)

print(triangles)

print(len(triangles))

print()

from itertools import permutations

for perm in permutations(triangles, 4):

    if  perm[0][2] != perm[1][0]:

        continue

    if  perm[1][2] != perm[2][0]:

        continue

    if  perm[2][2] != perm[3][0]:

        continue

    print(perm)