The perimeter of a triangle ABC is 105 cm. The altitudes AD, BE and CF are in the ratio 3 : 5 : 6. What is AB : BC : CA equal to?

Area = (1/2) × base × height is the same for all three altitudes. So BC × AD = CA × BE = AB × CF. If altitudes are in ratio 3 : 5 : 6 (from A, B, C), then opposite sides are in inverse ratio: BC : CA : AB = 1/3 : 1/5 : 1/6 = 10 : 6 : 5. So AB : BC : CA = 5 : 10 : 6. Hmm, let me recheck. AD is altitude from A to BC, so BC × AD = 2·Area, meaning BC ∝ 1/AD. Sides BC, CA, AB ∝ 1/3, 1/5, 1/6 = 10, 6, 5. So BC : CA : AB = 10 : 6 : 5, giving AB : BC : CA = 5 : 10 : 6. Answer (b).