Answer
$i=36cm$
Work Step by Step
Since the lens is converging, the focal length is positive (f=20cm). Use the lens equation $$\frac{1}{f}=\frac{1}{i}+\frac{1}{p}$$ to solve for $i$. $$\frac{1}{i}=\frac{p}{pf}-\frac{f}{pf}$$ $$\frac{1}{i}=\frac{p-f}{pf}$$ $$i=\frac{pf}{p-f}$$ Substituting values of $f=20cm$ and $p=45cm$ yields an image distance of $$i=\frac{(45cm)(20cm)}{45cm-20cm}=36cm$$
