Step-by-step explanation:
54^2 + a^2 = 90^2
2916 + a^2 = 8100
a^2 = 8100 - 2916
a^2 = 5184
take the square root of 5184
a = 72
you could have also guessed that its a 3 4 5 right triangle
all the sides are multiples of 3 4 or 5
The augmented matrix is
![\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%263%262%261%2610%5C%5C2%26-4%268%263%2610%267%5C%5C3%26-6%2610%266%265%2627%5Cend%7Barray%7D%5Cright%5D)
Add -2(row 1) to row 2, and add -3(row 1) to row 3:
![\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&-1&8&-13\\0&0&1&0&2&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%263%262%261%2610%5C%5C0%260%261%26-1%268%26-13%5C%5C0%260%261%260%262%26-3%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 2) to row 3:
![\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&-1&8&-13\\0&0&0&1&-6&10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%263%262%261%2610%5C%5C0%260%261%26-1%268%26-13%5C%5C0%260%260%261%26-6%2610%5Cend%7Barray%7D%5Cright%5D)
Add row 3 to row 2:
![\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&0&2&-3\\0&0&0&1&-6&10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%263%262%261%2610%5C%5C0%260%261%260%262%26-3%5C%5C0%260%260%261%26-6%2610%5Cend%7Barray%7D%5Cright%5D)
Add -3(row 2) to row 1, and add -2(row 3) to row 1:
![\left[\begin{array}{ccccc|c}1&-2&0&0&7&-1\\0&0&1&0&2&-3\\0&0&0&1&-6&10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%260%260%267%26-1%5C%5C0%260%261%260%262%26-3%5C%5C0%260%260%261%26-6%2610%5Cend%7Barray%7D%5Cright%5D)
Unusual question. 4/5 = 0.8, which is NOT a repeating decimal; it's a rational fraction.