The radii r1,r2,r3 of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24cm2 and its perimeter is 24cm, then the length of its largest side is
A
10
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A10 Given r1,r2,r3 are in H.P. Thus, s−a△,s−b△,s−c△ are in A.P.
Or, s−a,s−b,s−c are in A.P.
Or, a,b,c are in A.P. and a+b+c=24=2s
Or, 2b+b=24,b=8⇒c=16−a
Also given √s(s−a)(s−b)(s−c)=24
Or √12(12−a)(12−8)(a−4)=24
Or (12−a)(a−4)=12
OR a2−16a+60=0⇒a=6,10