An equation from Diophantus I can't seem to solve properly

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. (Headbang)

P.S. Answers are complex, FYI.

Re: An equation from Diophantus I can't seem to solve properly

Quote:

Originally Posted by

**Grep** 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. (Headbang)

P.S. Answers are complex, FYI.

I am reading that very book and I have arrived at the appropriate equation. Paul Nahin (the author) simplifies Diophantus' reduced equation .

First bring 1/x and 14x to the other side of the equation to simplify the radical. so

Which is the solution Pual Nahin noted

Your answer is correct if you define x to be 1/x (which is what Diophantus did for the area P1P2=14=14, he defined P1=1/x and P2= 14x)