Problem : In the figure below, BDEF is a square inscribed in the right triangle ABC. Given the sides of the triangle, find the length x of the side of the square.
Solution to Problem :
 The sum of the areas of triangles BEC and BEA is equal to the total area of the right triangle which is (1/2)*40*30 = 600. Let x be the length of the side of the square, hence
Area of BEC = (1/2)*40*x = 20x
Area of BEA = (1/2)*30*x = 15x
 We now write an equation using total area and solve for x
20x + 15x = 600
x = 120 / 7 = 17.1
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