Megha made two similar kites. The diagonal of the bigger kite is $1.5$ times the diagonal of the smaller kite.

In the smaller kite, the two diagonals are: $\mathrm{BD}=40 \mathrm{cm}$ and $\mathrm{AC}=68 \mathrm{cm}$. Find the length of the bigger diagonal of the bigger kite (in $\mathrm{cm}$).

A restaurant serves two sizes of sandwiches in their menu: Large and Extra Large

The sandwiches are in the shapes of equilateral triangles. To make these, the chefs will need two different sizes of breads. 

The Large Size sandwich has an area of $81 {\mathrm{cm}}^2$ and can be made with a bread loaf with side length $12 \mathrm{cm}$.

If the area of the Extra Large Sandwich is $225 {\mathrm{cm}}^2$, then find the length of bread loaf (in $\mathrm{cm}$) which the chef will need to use.