Geometry+Algebra=Fun

Geometry Level 5

△ABC has side lengths 4, 51 and 53. Each of its sides are trisected and lines are drawn to each point of trisection from their corresponding angle. By doing this, a hexagon is created in the middle of the triangle. The area of this hexagon can be represented by p = x (x-1)(x-2)² + x and

p =((y² cos(60∘)/asin(1))/x²(10+10))-y²-4² where x and y are integers and p is the area of the hexagon. What would the hypotenuse squared of a right-angled triangle be if x+y and were the values of the two remaining sides?

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