## syhna 2 years ago find the radius of the largest circle that can be inscribed in a triangle with sides 5 cm, 7 cm, 10 cm respectively

1. matricked

let r be the radius of the largerst circle that can be drawn inside traingle then area of the triangle is given by the sum of the three triangles thus formed by joining the incentre with the respective vertices

2. matricked

thus r = area of triangle /(semi-perimeter of the triangle)

3. matricked

area of triangle= sqrt(11*1*6*4)=sqrt (264) =16.248 semi-perimetr= (5+7+10)=22/2=11 thus r =16.248/11 =1.477

4. syhna

i dont get it? i also solved it but in a different solution but i wasn't sure of my answer so i asked the question but our solutions and answers did not match so will you explain to me your solution ? pleeaase?

5. matricked

see first of all roughly draw the incircle touching all the sides of the triangle

6. matricked

now take any one side and see it forms a triangle with the incentre as one of the vertex and the side of the triangle as the base

7. syhna

|dw:1358145014344:dw| is the drawing supposed to be like this?

8. matricked

if i assume the lengths of the sides to be a,b,c (and say a=5,b=7,c=10) and r be the incenter of the triangle ,. then area of triangle is given by area =sqrt(s*s-a)*(s-b)*(s-c)) also when the triangle is subdivided into three tr

9. syhna

|dw:1358145137085:dw|

10. syhna

A = sqrt(11(11-5)(11-7)(11-10) right?

11. matricked

yup

12. matricked

also if r is the incentre then area=1/2 *r *5 + 1/2 *r *7 + 1/2 *r *10 =r *(5+7+10) /2 =r*22/2=11 *r hence 11r =sqrt(11(11-5)(11-7)(11-10) or r = (sqrt(11(11-5)(11-7)(11-10))/11

13. matricked

u can correct or check the calcualtion

14. syhna

1.47 cm?

15. syhna

thanks :)

16. matricked

welcome