Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

is the drawing supposed to be like this?

Answer 8

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

Answer 9

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

right?

Answer 10

yup

Answer 11

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

Answer 12

u can correct or check the calcualtion

Answer 13

1.47 cm?

Answer 14

thanks :)

Answer 15

welcome