Difference between revisions of "2007 iTest Problems/Problem 7"
(New page: ==Problem== An equilateral triangle with side length <math>1</math> has the same area as a square with side length <math>s</math>. Find <math>s</math>. <math>\mathrm{(A)}\,\frac{\sqrt[4]{...) |
(No difference)
|
Revision as of 10:59, 16 December 2007
Problem
An equilateral triangle with side length 
has the same area as a square with side length 
.
Find .
![$\mathrm{(A)}\,\frac{\sqrt[4]{3}}{2}\quad\mathrm{(B)}\,\frac{\sqrt[4]{3}}{\sqrt{2}}\quad\mathrm{(C)}\,1\quad\mathrm{(D)}\,\frac{3}{4}\quad\mathrm{(E)}\,\frac{4}{3}\quad\mathrm{(F)}\,\sqrt{3}\quad\mathrm{(G)}\,\frac{\sqrt6}{2}$](http://latex.artofproblemsolving.com/0/f/d/0fd9825fdc1605c6a9bd15b665c79728f942f87c.png)
Solution
An equilateral triangle with side length 1 has an area of 
, and a square with that area has a side length of $\sqrt{\frac{\sqrt{3}}{4}=\frac{\sqrt[4]{3}}{2} \Rightarrow \mathrm{(B)}$ (Error compiling LaTeX. Unknown error_msg)
