JEE Main Maths: Triangles questions with solutions

Q1. Triangle ABC has a right angle at B, with AB = 3 and hypotenuse AC = 5. Point D is on side BC such that BD/DC = AB/AC. Find the length AD.

1. 4*sqrt(3)/3
2. 3*sqrt(5)/2
3. 4*sqrt(5)/3
4. 5*sqrt(3)/4

Answer: 3*sqrt(5)/2

BC = 4 (Pythagoras). BD/DC = 3/5 so BD = (3/8)*4 = 3/2. In right triangle ABD: AD = sqrt(AB² + BD²) = sqrt(9 + 9/4) = sqrt(45/4) = 3*sqrt(5)/2.