The area of the smaller triangle is about 270 ft2. Which is the best approximation for the area of the larger triangle?

the assumption here is that, both triangles are similar.  Now, if that's the case,

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{small}{large}\qquad \cfrac{25}{35}\implies \stackrel{simplified}{\cfrac{5}{7}}\qquad \qquad \cfrac{5}{7}=\cfrac{\sqrt{270}}{\sqrt{x}}\implies \cfrac{5}{7}=\sqrt{\cfrac{270}{x}} \\\\\\ \left( \cfrac{5}{7} \right)^2=\cfrac{270}{x}\implies \cfrac{5^2}{7^2}=\cfrac{270}{x}\implies x=\cfrac{7^2\cdot 270}{5^2}[/tex]