document.write( "Question 1121142: A square and an equilateral have equal perimeter. If the area of the triangle is 9 sqrt(3) cm squared, find the exact length of the diagonal of the square. \n" ); document.write( "

Algebra.Com's Answer #736915 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The area of an equilateral triangle with side length s is $\"%28s%5E2%29%2A%28sqrt%283%29%2F4%29\"$ .

\n" ); document.write( "Give that the area of the triangle is 9*sqrt(3), the side length is 6:
\n" ); document.write( " $\"%28s%5E2%29%2A%28sqrt%283%29%2F4%29+=+9%2Asqrt%283%29\"$ --> $\"s%5E2%2F4+=+9\"$ --> s = 6.

\n" ); document.write( "Now find the perimeter of the triangle, which is the same as the perimeter of the square; so you can find the length of a side of the square and then find the length of the diagonal. \n" ); document.write( "

\n" );