ABC is a triangle right
angled at C. Three semicircles are drawn
on the sides AB, BC and CA as the respective diameters. If the sides a, b, c of the triangle are positive
integers and the sum of the shaded areas is also to be a positive integer, how
many distinct such triangles are there with perimeter at most 60 units?
3 comments:
Sir, 9 triangles are possible.
the shaded areas lie between 3 semi circles and the circumcircle of triangle which equal(after simplify)1/4(22/7)(a+b)+(1/2)ab.so (a+b)must be the multiple of 7 and even then,(a=6 ,b=8)or (a=12 ,b=16)
This question can be independently asked as to find the number of Pythagorean triplets whose sum is less than or equal to sixty. But the idea was to connect the shaded area to the area of the triangle.
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