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If in any tri...

Question

If in any triangle the sides a,b,c are respectively 13, 14, 15, then $r_{1}$ = ...., $r_{2}$ = ...., $r_{3}$ = ....

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Solution

Given: a=13 cm, b=14 cm, c=15 cm
$⟹ s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = 21$ cm
Now, $S = \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{21 \times 8 \times 7 \times 6} = 7 \times 3 \times 2 \times 2 = 84 {c m}^{2}$
$r_{1} = \frac{S}{s - a} = \frac{84}{8} = \frac{21}{2} = 10.5 c m r_{2} = \frac{S}{s - b} = \frac{84}{7} = 12 c m r_{3} = \frac{S}{s - c} = \frac{84}{6} = 14 c m$

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