Question

What is the maximum number of equilateral triangles of side $3cm$ that can be fitted in a large equilateral triangle with length $11.2cm$?

Answer 1

$\begin{array}{c}Atfirst\\ a=3\\ areaofequilateraltriangle=\frac{\sqrt{3}}{4}{\left(side\right)}^2\\ =\frac{\sqrt{3}}{4}{\left(3\right)}^2\\ Now,again\\ A=11.2cm\\ Areaofequilateraltriangle=\frac{\sqrt{3}}{4}{\left(side\right)}^2\\ =\frac{\sqrt{3}}{4}{\left(11.2\right)}^2\\ Now,\\ No.ofmaximumnumberofequlateraltriangles=\frac{\frac{\sqrt{3}}{4}\times 11.2\times 11.2}{\frac{\sqrt{3}}{4}\times 3\times 3}\\ =\frac{11.2\times 11.2}{3\times 3}\\ =\frac{125.44}{9}\\ =13.93\sim 14\\ Hence,thenumberofmaximumequlateraltriane=13\end{array}$