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7 similar triangles are arranged side by side in a clockwise spiral. The short sides of each triangle forms the hypotenuse of the next triangle . Each triangle is isosceles and has a right angle. The lengths of the hypotenuses are l, l2, l3,… where 0<l<1.
Show that l2=21.
Hence find the total area of the 7 triangles, giving your answer in the form 2m2n−k where n,k and m∈N.
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