Exams › JEE Main › Maths

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

Correct answer: 3*sqrt(5)/2

Solution

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.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →