document.write( "Question 607558: The side of a square is four times as long as the base of the triangle. If the areas of the triangle and square are equal, determine the ratio of the height of the triangle to the side of the square. \n" ); document.write( "

Algebra.Com's Answer #382817 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The side of a square is four times as long as the base of the triangle.
\n" ); document.write( " If the areas of the triangle and square are equal, determine the ratio of the height of the triangle to the side of the square.
\n" ); document.write( ":
\n" ); document.write( "Let x = the base of the triangle
\n" ); document.write( "then
\n" ); document.write( "4x = the side of the square
\n" ); document.write( ":
\n" ); document.write( "Let h = height of the triangle
\n" ); document.write( ":
\n" ); document.write( "triangle area = square area
\n" ); document.write( ".5*x*h = (4x)^2
\n" ); document.write( ".5*x*h = 16x^2
\n" ); document.write( "h = $\"%2816x%5E2%29%2F%28.5x%29\"$
\n" ); document.write( "cancel .5x into 16x^2
\n" ); document.write( "h = 32x
\n" ); document.write( ":
\n" ); document.write( "\"determine the ratio of the height of the triangle to the side of the square.\"
\n" ); document.write( " $\"h%2F%284x%29\"$
\n" ); document.write( "replace h with 32x
\n" ); document.write( " $\"%2832x%29%2F%284x%29\"$ = 8:1 \n" ); document.write( "

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