Answer:
AI = 34
Explanation:
If I is the incentre, then AI, BI, and CI, are radii of the incircle.
They are all equal.
AI = BI = CI
3x + 7 = 5x - 11 = 52 -2x
Consider AI and BI
3x + 7 = 5x - 11
Add 11 to each side
3x + 18 = 5x
Subtract 3x from each side
2x = 18
Divide each side by 2
x = 9
AI = 3x + 7 = 3 × 9 +7 =27 +7 = 34
Check:
BI = 5x - 11 = 5 × 9 - 11 = 45 - 11 = 34
CI = 52 - 2x = 52 - 2× 9 = 52 - 18 = 34