Hard Question

This one is (a little) difficult

Note that...if we square both sides, we get

h^2 - a^2  =  24^2

h ^2 - a^2  = 576

(h + a) ( h  - a)  =  576

We need to find all the divisors of   576.....here they are :

1 | 2 | 3 | 4 | 6 | 8 | 9 | 12 | 16 | 18 | 24 | 32 | 36 | 48 | 64 | 72 | 96 | 144 | 192 | 288 | 576

Now, we need to consider  all the pairs that multiply to 576  ......and we need to be able to split one of the pairs such that the difference of this split  is equal to the other member in the original pair

Note...the larger number in the original pair is the one we want to split....!!!!

Let me get you started....we can work from the "outside-in" to find all the possible pairs that multiply to 576

Pair  

576  , 1     no way to split the first number such that the difference of this split = 1

288, 2        split 288 into 145, 143.....their difference = 2

Note that  ( 145 +143) ( 145 - 143)   = 576

192, 3     no  way to split the first number  such that the difference of this split = 3

144, 4        note that 144 spits into  74, 70   .....their difference = 4

Note that (74 + 70)(74 - 70)  =  576

96, 6          51, 45 is the split  we need

(51 + 45) (51 - 45) = 576

You should find  4 more workable pairs....if you get stuck...let me know!!!