I was given this problem by a friend a few days ago, and I still haven't bee able to figure it out.
You are given a trapezoid ABCD, and a right triangle ADE, figure out the length of the line AE, from the lengths of the lines AD and BC. The angles BCD, CDA, and ADE are all right angles, and the sides of the trapezoid AB and BC are the same length.
I'm guessing my friend wants an equation in terms of AE = f(AD,BC). Please help me find the equation, I'm honestly stumped at this point :\ . Thanks!
From similarity of triangles EAD and EBC $$\frac vy = \frac{v+x}x$$ hence $$vx= vy + xy$$ $$v(x-y)= xy$$ and $$v= \frac{xy}{x-y}=\cfrac 1{\cfrac 1y-\cfrac 1x}$$