In geometry test 1, the soln for "Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?" makes no sense to me. they have solved using Pythagoras theorem on a scalene triangle. Please look into it.

Hi Olivia,
The solution is correct. If you refer to the figure given in the solution, the required triangle is AMB. AO is the height of the triangle AMB. Right angled triangle AOB has been constructed to simplify the calculation. If you did not understand the method you can also do it using Heron's Formula but it will complicate the calculations, so this is the best method to solve this question. If any specific step is still not clear, please point that out.
Thanks.