Question

Area of a triangle is $60c{m}^2$ and the ex-radii are $4cm,6cm,10cm$ respectively. The measure of the sides of the triangle are:

• A. $15cm,20cm,24cm$
• B. $16cm,21cm,25cm$
• C. $15cm,21cm,30cm$
• D. $13cm,19cm,25cm$

Answer 1

Answer: (B)

$16cm,21cm,25cm$

$\Delta =60c{m}^2,r_1=4cm,r_2=6cm,r_3=10cm$

$r_1=\frac{\Delta }{s-a}⟹s-a=\frac{60}{4}=15cm$

$r_2=\frac{\Delta }{s-b}⟹s-b=\frac{60}{6}=10cm$

$r_3=\frac{\Delta }{s-c}⟹s-c=\frac{60}{10}=6cm$

$s-a+s-b+s-c=s=15+10+6=31$

$a=s-15=16b=s-10=21c=s-6=25$