SOLUTION: 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

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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?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
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.
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.
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.
Then by adding up all the cut off parts, the total area is
2%2A%28y%5E2%2F2%29+%2B+2xy+%2B+2%2A%28x%5E2%2F2%29+=+800
==> x%5E2+%2B+2xy+%2B+y%5E2+=+800 <==> %28x%2By%29%5E2+=+800
==> x%2By+=+20%2Asqrt%282%29
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.