An equilateral triangle of side length $10$ is completely filled in by non-overlapping equilateral triangles of side length $1$. How many small triangles are required?
$\mathrm{(A)}\ 10\qquad\mathrm{(B)}\ 25\qquad\mathrm{(C)}\ 100\qquad\mathrm{(D)}\ 250\qquad\mathrm{(E)}\ 1000$
The area of the large triangle is $\frac{10^2\sqrt3}{4}$, while the area of each small triangle is $\frac{1^2\sqrt3}{4}$. Dividing these two quantities results in $100$, therefore $\boxed{100} \mathrm{(C)}$ small triangles can fill the large one without overlap.