The perimeter of ΔABC is 27 cm and its side, BC = 12 cm. AD is the bisector of ∠BAC, while I is the incentre. AI : ID is equal to.

5 : 4

Perimeter of ΔABC = AB + BC + CA = 27 cm

and BC = 12cm

Here,

AB + BC + CA = 27 cm

AB + 12 + CA = 27 cm

AB + CA = 27 - 12 = 15

We know that,

AI : ID = (AB + AC) : BC

           = (15) : 12

           = 5 : 4

AI : ID = 5 : 4