diameter

The sides of a triangle are 25,39 and 40 . What is the diameter of the circumscribed circle?

Any help would be appreciated

Note by Rohit Udaiwal
3 years, 1 month ago

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We can use the formula from this link, namely

\(R = \dfrac{abc}{4A} \Longrightarrow D = \dfrac{abc}{2A},\)

where \(a,b,c\) are the side lengths of the triangle and \(A\) is its area. To find the area, we can use Heron's formula

\(A = \sqrt{s(s - a)(s - b)(s - c)}\) where \(s = \dfrac{a + b + c}{2}.\) In this case \(s = \dfrac{25 + 39 + 40}{2} = 52,\) and so

\(A = \sqrt{52*27*13*12} = 468,\) resulting in \(D = \dfrac{25*39*40}{2*468} = \dfrac{125}{3}.\)

Brian Charlesworth - 3 years, 1 month ago

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Thanks a lot sir! \[\huge\ddot\smile\]

Rohit Udaiwal - 3 years, 1 month ago

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