$$ Length\ of\ 2\ similar\ triangles=4:5=\frac{4}{5} $$

and

$$ Hypotenuse\ of\ smaller\ triangle=24\ inches $$

We have to find the length of hypotenuse of larger triangle.

$$ \therefore \frac{h}{24}=\frac{5}{4} $$

$$ =\frac{24\times5}{4}=30 $$

So choice E is correct.