diameter

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

Any help would be appreciated

#Geometry

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Comments

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 - 5 years, 10 months ago

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

Rohit Udaiwal - 5 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$