AP EAMCET201923 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual
In triangle (A B C ), if (r₁=36, r₂=18 ) and (r₃=12 ), then (a+b= )
Options
- A36
- B24
- C30
- D54
Correct answer
D. 54
Step-by-step solution
It is given in a ( A B C ) ( aligned & r₁= s-a =36, r₂= s-b =18 and r₃= s-c =12 & 1 r₁ + 1 r₂ + 1 r₃ = 1 36 + 1 18 + 1 12 = 1+2+3 36 = 1 6 & s-a+s-b+s-c = 1 6 & s = 1 6 =6 s aligned ) So, (r₁= s-a = 6 s s-a =36 s=6 s-6 a 6 a=5 s ) (r₂= s-b = 6 s s-b =18 s=3 s-3 b 3 b=2 s ) and (r₃= s-c = 6 s s-c =12 s=2 s-2 c 2 c=s ) So, ( ^2=36 s^2 ) ( array lrl & s(s-a)(s-b)(s-c)=36 s^2 & (s- 5 s 6 ) (s- 2 s 3 ) (s- s 2 )=36 ~s & s^3 ( 1 6 ) ( 1 3 ) ( 1 2 )=36 s & s^2=(36)^2 s=36 & a & =30 and b=24 array ) So, (a+b=30+24=54 ) Hen