In a triangle abc the incircle touches the sides bc,ca and ab respectively at d,e and f.if the radius of the incircle is 4units and if bd,ce and af are consecutive integers,find the sides of triangle abc
Answers
bc = 13 , ac = 15 , ab = 14 if In a triangle abc the incircle touches the sides bc,ca and ab respectively at d,e and f. and the radius of the incircle is 4units and bd,ce and af are consecutive integers
Step-by-step explanation:
bd = n
ce = n + 1
af = n+2
bf = bd = n
ae = af = n + 2
cd = ce = n + 1
bc = bd + cd = n + n + 1 = 2n+1
ac = ae + ce = n+2 + n + 1 = 2n + 3
ab = af + bf = n + 2 + n = 2n + 2
s = (2n + 1 + 2n + 3 + 2n + 2) /2
= 3n + 3
= 3(n + 1)
Area of Triangle =√3(n+1)(n+2)(n)(n+1)
= (n + 1)√3n(n+2)
Area of traingle = (1/2) (bc + ac + ab) * r
r = 4
= (1/2)(6(n+1) * 4
= 12(n + 1)
(n + 1)√3n(n+2) = 12(n + 1)
=> √3n(n+2) = 12
Squaring both sides
=> 3n(n + 2) = 144
=> n² + 2n - 48 = 0
=> n² + 8n - 6n - 48 = 0
=> (n + 8)(n - 6) = 0
=> n = 6 ( can not be - ve)
bc = 13 , ac = 15 , ab = 14
Learn more:
prove that if the hypotenuse of a right triangle is h and the radius of ...
https://brainly.in/question/13221257
∆ABC is an isosceles triangle.Its perimeter is 44 cm and base BC ...
https://brainly.in/question/11793384