document.write( "Question 892106: a rectangle remains after an isosceles right triangle is removed from each corner of square piece of paper. if the sum of the areas of the cut off pieces is 800 square units, what is the length of diagonal of the rectangle?
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Algebra.Com's Answer #540311 by robertb(5830) $\"\"$ $\"About$

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Let the legs of one isosceles triangle have length of y units each. There are two of these triangles, both lying on opposite corners of the square.
\n" ); document.write( "Let the legs of the other isosceles triangle have length of x units each. There are two of these triangles, likewise lying on the other opposite corners of the square.
\n" ); document.write( "The diagonal of the first isosceles triangle is $\"sqrt%282%29%2Ay\"$ units, while the isosceles triangle in the adjacent corner is $\"sqrt%282%29%2Ax\"$ units. The area of rectangle formed is $\"sqrt%282%29%2Ay%2Asqrt%282%29%2Ax+=+2xy\"$ .
\n" ); document.write( "Then by adding up all the cut off parts, the total area is\r
\n" ); document.write( "\n" ); document.write( " $\"2%2A%28y%5E2%2F2%29+%2B+2xy+%2B+2%2A%28x%5E2%2F2%29+=+800\"$
\n" ); document.write( "==> $\"x%5E2+%2B+2xy+%2B+y%5E2+=+800\"$ <==> $\"%28x%2By%29%5E2+=+800\"$
\n" ); document.write( "==> $\"x%2By+=+20%2Asqrt%282%29\"$
\n" ); document.write( "But x + y is the side of the square, and so its diagonal is given by $\"sqrt%282%29%2A%28x%2By%29\"$ . Therefore, diagonal of square is $\"sqrt%282%29%2A20%2Asqrt%282%29+=+40\"$ units. \n" ); document.write( "

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