Answer: D

Small Hint:

A diagonal’s horizontal projection is half the sum of the two bases

Big Hint:

Scale the larger base to $1$, and let the smaller base and altitude both be $r$

Solution:

Let the larger base be $1,$ and let the smaller base and altitude both be $r.$ A diagonal has horizontal projection $\frac{1+r}{2}$ and length $1.$ Thus $$1=r^2+\left(\frac{1+r}{2}\right)^2.$$ This simplifies to $$\begin{aligned} 5r^2+2r-3&=(5r-3)(r+1)\\ &=0. \end{aligned}$$ The positive ratio is $r=\frac{3}{5}.$

Thus, the correct answer is D.