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Maths-

General

Easy

Question

If the sides of triangles are $8 comma 15 comma 17$ then radius of the Circumcentre is

$15 / 2$
$13 / 2$
$5 / 2$
$17 / 2$

hint Hint:

In this question we can see that the sides of the triangle are pythagorean triplet. So, the triangle will be Right angle triangle. The radius of a Circumcircle for a right angle triangle is half the length of the hypotenuse.

The correct answer is: $17 divided by 2$

In this question we have to find the radius of the circumcentre.
Step1: Using Pythagoras theorem
The sides of the triangle are given as $15 comma 8 comma 17$ .
$17 squared equals 289 15 squared equals 225 8 squared equals 64$
We can easily see that $17 squared equals 15 squared plus 8 squared$ .
Hence, the given triangle is right angle triangle with hypotenuse side being $17$
Step2: Radius of Circumcircle.
In a right angle triangle the radius of circumcircle is half the length of the hypotenuse of the triangle.
That is $r a d i u s space equals space fraction numerator h y p o t e n u s e over denominator 2 end fraction$
radius = $17 over 2$
So, the radius of circumcircle is $17 over 2$ .

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