if a + b + C is equal to 15 and a b + BC + AC is equal to 60 then find the value of a square + b square + c square
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(a + b + c) = 15
Square on both sides,
(a + b + c)² = (15)²
a² + b² + c² + 2(ab + bc + ca) = 225
a² + b² + c² + 2(60) = 225
a² + b² + c² + 120 = 225
a² + b² + c² = 225 - 120
a² + b² + c² = 105
Square on both sides,
(a + b + c)² = (15)²
a² + b² + c² + 2(ab + bc + ca) = 225
a² + b² + c² + 2(60) = 225
a² + b² + c² + 120 = 225
a² + b² + c² = 225 - 120
a² + b² + c² = 105
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the sides of triangle are 35cm,54cm,61cm.find the length of its longest altitude
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