Length of a right triangle created by skewing a rectangle's edge by a fixed amount

Question

I have the above problem for a grid-based graphics system I'm working on, and I'm not sure if the math is solvable or not.

I'm trying to determine the value of $A$. I've attempted to use substitution and Pythagoras to relate the 4 variables to each other and come to an equation only containing $A$:

My result was:

$$\sqrt{98.015094971 - 20.6896201A + A^2} + A = 10$$

which does not appear solvable by the algebra tool I was leveraging (cymath).

Some advice here would be much appreciated. Is this problem unsolvable (which means I will resort to empirical testing to determine an acceptable $A$ value) or is there another approach?

Thanks!

Answer 1

You can use similarity :

The big $\triangle$ with sides $3,D,C$ $\sim$ Small $\triangle$ with sides $A, B, 0.5$ $$\frac{0.5}{x}=\frac{3}{10-x}$$ $$10-x=6x$$ $$7x=10$$ $$x=10/7=1.428$$

Answer 2

Thales theorem :

$\frac{0.5}{3+0.5}=\frac{a}{a+c}$

$\frac{1}{7}=\frac{a}{a+c}$

$7a=a+c=10$

$a=\frac{10}{7}$