A triangle has sides with lengths of 5, 7, and 4. What is the radius of the triangles inscribed circle?

Question

A triangle has sides with lengths of 5, 7, and 4. What is the radius of the triangles inscribed circle?

1 Answer

Impact of this question

2630 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-24T07:45:36

$R a d i u s$ $Radius$ $o$ $o$ $f$ $f$ $c i r$ $cir$ $c l$ $cl$ $e$ $e$ = $\frac{\sqrt{6}}{2}$ $sqrt6/2$

Explanation:

$R a d i u s$ $Radius$ $o$ $o$ $f$ $f$ $c i r$ $cir$ $c l$ $cl$ $e$ $e$ $i$ $i$ $n s c r i b e d$ $nscribed$ $i$ $i$ $n s i d e$ $nside$ $a$ $a$ $△$ $triangle$ = $(A r e a$ $(Area$ $o$ $o$ $f$ $f$ $△)$ $triangle)$ $/$ $/$ $s$ $s$
$W h e r e$ $Where$ $s = s e m i$ $s=semi$ $p e r i m e t e r$ $perimeter$ $o$ $o$ $f$ $f$ $△$ $triangle$

$s = \frac{5 + 7 + 4}{2} = \frac{16}{2} = 8$ $s=(5+7+4)/2=16/2=8$

$a = 5, b = 7, c = 4$ $a=5,b=7,c=4$

$A r e a$ $Area$ $o$ $o$ $f$ $f$ $△$ $triangle$ = $\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt[s(s-a)(s-b)(s-c)]$

$\to = \sqrt{8 (8 - 5) (8 - 7) (8 - 4)}$ $rarr=sqrt[8(8-5)(8-7)(8-4)]$

$\to = \sqrt{8 (3) (1) (4)}$ $rarr=sqrt[8(3)(1)(4)]$

$\to = \sqrt{8 (96)}$ $rarr=sqrt[8(96)]$

$\to = \sqrt{96}$ $rarr=sqrt96$

$S o, R a d i u s$ $So,Radius$ $o$ $o$ $f$ $f$ $c i r$ $cir$ $c l$ $cl$ $e$ $e$ $= \frac{\sqrt{96}}{8} = \frac{2 \sqrt{24}}{8} = \frac{\sqrt{24}}{4} = \frac{2 \sqrt{6}}{4} = \frac{\sqrt{6}}{2}$ $=sqrt96/8=(2sqrt24)/8=sqrt24/4=(2sqrt6)/4=sqrt6/2$

Science

Math

Humanities

... and beyond

A triangle has sides with lengths of 5, 7, and 4. What is the radius of the triangles inscribed circle?

1 Answer

Explanation:

Related questions

Impact of this question