document.write( "Question 747785: A square is divided into three equal area by two parpllel lines drawn from opposite vertices.Determine the square in cm square if the distance between the two lines is 1 cm ? \n" ); document.write( "

Algebra.Com's Answer #852552 by greenestamps(13261) $\"\"$ $\"About$

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\n" ); document.write( "Drawing the figure as described, we see the square divided into two congruent right triangles and a parallelogram, with all three figures having the same area.

\n" ); document.write( "Let x be the side length of the square.

\n" ); document.write( "The area of each right triangle is one-third the total area of the square, $\"%281%2F3%29x%5E2\"$

\n" ); document.write( "The length of one leg of the triangle is x; the length of the other leg is such that the area of the triangle -- one-half the product of the lengths of the two legs -- is $\"%281%2F3%29x%5E2\"$ . That makes the length of the other leg $\"%282%2F3%29x\"$

\n" ); document.write( "With legs of lengths $\"x\"$ and $\"%282%2F3%29x\"$ , the length of the hypotenuse, from the Pythagorean Theorem, is $\"x%2Asqrt%2813%29%2F3\"$

\n" ); document.write( "Drawing an altitude of length 1 of the parallelogram produces a right triangle, similar to the two large triangles, with long leg of length 1 and hypotenuse of length $\"x%2F3\"$ .

\n" ); document.write( "Using corresponding parts of similar triangles, we then have

\n" ); document.write( " $\"%28x%2F3%29%2F1=%28x%2Asqrt%2813%29%2F3%29%2Fx\"$

\n" ); document.write( " $\"x%2F3=sqrt%2813%29%2F3\"$

\n" ); document.write( " $\"x=sqrt%2813%29\"$

\n" ); document.write( "The side length of the square in centimeters is $\"sqrt%2813%29\"$ , so the area of the square in square centimeters is 13.

\n" ); document.write( "ANSWER: 13

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