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Paul Andrews, a respected mathematics educator based at Cambridge University, explains why he likes this problem :
Challenge students to find a general method for working out how many different isosceles triangles can be drawn for any given area (assuming we retain all the other constraints).
Determine the total shaded area of the 'kissing triangles'.
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?