This is driving me nutty. I'm solving an equation from Diophantus, and I keep ending up with what appears to be wrong, and yet I can't see where. I must be messing up something pretty basic here. Help highly appreciated! Ok, the problem is:
Given a right triangle with area 7 and perimeter 12. Find it's sides.
Let x and y be the sides next to the right angle.
So, the area is or and perimeter is
First, I try to get rid of the radical in the second equation by isolating it on one side and squaring both sides of the equation:
I turn the first equation into and substitute into the other equation:
Multiplying everything by x to get rid of the 336/x, I get:
However, the book (The Story of ) says it's
I must have made an error but I don't see it. I know I need to go to sleep, but I'll probably be having trouble sleeping with that bothering me.
P.S. Answers are complex, FYI.