Question #15b51

Question

Question #15b51

1 Answer

Impact of this question

2029 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-25T03:42:15

$a = 2 \sqrt{489}$ $a=2sqrt489$

Explanation:

Let $r$ $r$ be the inradius of the triangle,
given that the area of the incircle $= 163 π$ $=163pi$ ,
$\Rightarrow π r^{2} = 163 π$ $=> pir^2=163pi$
$\Rightarrow r = \sqrt{163}$ $=> r=sqrt163$

Formula for inradius ( $r$ $r$ ) of a triangle : $r = \frac{2 A}{p}$ $r=(2A)/p$ ,
where $A and p$ $A and p$ are the area and the perimeter of the triangle, respectively.
Recall that area $A$ $A$ of an equilateral triangle is : $A = \frac{\sqrt{3} a^{2}}{4}$ $A=(sqrt3a^2)/4$ ,
where $a$ $a$ is the side length of the equilateral triangle.
$\Rightarrow r = \frac{2 A}{p} = \frac{\frac{2 \cdot \sqrt{3} a^{2}}{4}}{3 a} = \frac{\sqrt{3} a}{6}$ $=> r=(2A)/p=((2*sqrt3a^2)/4)/(3a)=(sqrt3a)/6$

$\Rightarrow \frac{\sqrt{3} a}{6} = \sqrt{163}$ $=> (sqrt3a)/6=sqrt163$
$\Rightarrow a = \frac{6 \sqrt{163}}{\sqrt{3}} = 2 \sqrt{489}$ $=> a=(6sqrt163)/sqrt3=2sqrt489$ units

Footnotes: formula for inradius $r$ $r$ of an equilateral traingle is given by :
$r = \frac{\sqrt{3}}{6} a$ $r=sqrt3/6a$ ,
where $a$ $a$ is the side length of the equilateral triangle.

Science

Math

Humanities

... and beyond

Question #15b51

1 Answer

Explanation:

Related questions

Impact of this question