Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2019MathematicsProperties of Triangles

In a triangle A B C , ∠ B A C = 90 ° ; A D is the altitude from A on to B   C . Draw D   E perpendicular to A   C and D   F perpendicular to A   B . Suppose A   B = 15 and B   C = 25   . Then the length of E   F is

Options

  1. A12
  2. B10
  3. C5 3
  4. D5 5

Correct answer

A. 12

Step-by-step solution

It is given that in triangle A B C , ∠ B A C = 90 ° , A D is the altitude from A on to B C. since, A B = 15 and B C = 25 ∴ A C = B C 2 - A B 2 = 625 - 225 Now, since area of ∆ A B C = 1 2 ( B C ) ( A D ) = 1 2 ( A B ) ( A C ) ⇒ 1 2 ( B C ) ( A D ) = 1 2 × 15 × 20 ⇒ 25 × A D = 300 ⇒ A D = 12 ∵ A E D F is a rectangle, then E F = A D = 12

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All KVPY PYQs