# 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 $$D = \dfrac{25*39*40}{2*468} = \dfrac{125}{3}.$$

- 3 years, 1 month ago

Thanks a lot sir! $\huge\ddot\smile$

- 3 years, 1 month ago