nkmungila wrote:

The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the

square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.comIf you know the formula for area of an equilateral triangle, the answer turns on translation and algebra.*

Area of an equilateral triangle, \(a\) = side:

\(\frac{a^2\sqrt{3}}{4}\)

"The area of an equilateral triangle [with side \(a\)] is \(\sqrt{3}\) times that of a square," with side \(s\). Translate:

(Area of square)(\(\sqrt{3}\)) = Area of triangle

\(s^2\sqrt{3}\) = \(\frac{a^2\sqrt{3}}{4}\)

Factor out \(\sqrt{3}\)

\(s^2 = \frac{a^2}{4}\)

\(\sqrt{s^2} = \sqrt{\frac{a^2}{4}}\)

\(s = \frac{a}{2}\)

Ratio of a side of the triangle to a side of the square? Rearrange the expression immediately above.

\(\frac{a}{s} = \frac{2}{1} = 2\)

Answer E

*

If you don't know the formula, although deriving it is painstaking, it is completely possible. You drop an altitude and find the area of two 30-60-90 right triangles, described here and here
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