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In the diagram above $\triangle{ABC}$ is an isosceles triangle with
$|\overline {\rm AB}| =|\overline {\rm BC}| = |\overline {\rm AC}| - 1 $. If the radius of the inscribed circle is $\dfrac{3}{2}$, find the area of $\triangle{ABC}$.

 Feb 5, 2021
 #1
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Inradius     r = 3/2 = 1.5   

 

Semiperimeter   s = (3x-1)/2

 

Triangle area     A = r (s)   

 

r = {sqrt[x2-((x-1)/2)2] *(x-1)/2 } / (3x-1)/2     

 

x = 3 + √7

 

I'll let you find the area of  ΔABC 

 Feb 5, 2021

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