Question

if area of square is 3 root 3 times the area of an equilateral triangle then the ratio of the side of the square to the side of the equilateral triangle is

Answer 1

Dear student,
$$\begin{gathered} Areaofsquare=3\sqrt{3}\times Areaofeqtriangle \\ \Rightarrow x^2=3\sqrt{3}\times \frac{\sqrt{3}}{4}\times a^2--[wherexandaaresidesofsquareandtrianglerespectively] \\ \Rightarrow x^2=\frac{9}{4}\times a^2 \\ \Rightarrow \frac{x^2}{a^2}=\frac{9}{4} \\ \Rightarrow \frac{x}{a}=\sqrt{\frac{9}{4}}=\frac{3}{2}--[neglecting-vevaluesassidescantbe-ve] \\ Thusratioofsideofsquaretosideoftriangleis3:2 \end{gathered}$$
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