Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side? ?->(Show Answer!)

1. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?

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By: anil on 05 May 2019 02.31 am

We know that area = 0.5*h*10 ; we get h = 16=oa. Using pythagoras we find $$ob^2+oa^2 = ab^2$$ $$ob^2+16^2 = 20^2$$ ob = 12 Using pythagoras in triangle oam we get am = $$sqrt {2^2 + 16^2 } $$ = $$sqrt {260}$$.

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