Tonia96TT said:
Hi Vela;
Thanks again for trying to help. For A I get A=(L^2-900)/L.
That's not what I have. I got
A = \frac{L^2 + 900}{2L}.
(I found it easier to leave in this form instead of simplifying further.)
If I plug this value into any of the other equations I get a nasty quadratic or even quartic (eg substitute the above into A^2 + C^2 = 50^2 and I get ((L^2-900)/L)^2 + C^2 = 50^2. Trying to find substitutions for C yield the same thing, and I still cannot isolate a single variable.
But you WILL end up an equation with a single variable, L. Solve for C in the same matter that you solved for A. You'll get that C = (some.expression.involving.L). Plugging in for BOTH A and C gets you
A^2 + C^2 = 50^2
\left( \frac{L^2 + 900}{2L} \right)^2 + (some.expression.involving.L)^2 = 50^2
(Of course, you'll have to find for yourself what "some.expression.involving.L" is.)
You mention quartics, and while it is true that your equation will be a quartic, the equation is still quadratic in form. Suppose you have a quartic that looks like this:
x^4 - 10x^2 + 29 = 0
If you let y = x^2, you'll get this:
y^2 - 10y + 29 = 0
... which is a quadratic. Here, you would solve for y, and then substitute y=x^2 back in, and solve for x. You'll have to do something similar eventually in this problem.
I am not sure I agree with your statement that "It works out quite easily", and would urge you to show me the complete solution in support of this.
It's against forum policy to show complete solutions. How do we know if you're telling the truth when you stated that this was not a homework question?
(I appreciate that folks are trying to walk me through this step by step with the goal of having me find the answer but I have been racking my brains over this for the better part of a week. Gentle nudges are lovely but it is time to call in the heavy artillery. I CANNOT find the solution, and would ask someone to spell it out for me as I no longer believe the solution is a simple one, and I challenge anyone to show me that it is.
Well, the solution is not "simple" in the sense that the answers are not integers. According to WolframAlpha you'll get multiple solutions, all of which are irrational. Of course, the negative ones will have to be eliminated.
But don't give up! I left you off with this:
A^2 + C^2 = 50^2
\left( \frac{L^2 + 900}{2L} \right)^2 + (some.expression.involving.L)^2 = 50^2
Find out what C is, and plug it in at "some.expression.involving.L" and simplify into a quartic. Show us what you got.