Join WhatsApp Icon JEE WhatsApp Group
Question 23

$$ABC$$ is a triangle and $$AD$$ is its altitude. If $$BD = 5DC$$, then the value of $$\frac{3(AB^2-AC^2)}{BC^2}$$ is


Correct Answer: 2

Solution

Share

Since $$AD$$ is the common altitude, $$AB^2-AC^2=BD^2-DC^2$$. Taking $$DC=x$$ and $$BD=5x$$ gives $$BC=6x$$ and $$BD^2-DC^2=25x^2-x^2=24x^2$$. So $$\frac{3(AB^2-AC^2)}{BC^2}=\frac{3(24x^2)}{36x^2}=2$$.

Get AI Help

Other Cracku’s Useful Resources:

JEE Questions JEE Question Bank JEE Mains Previous Papers JEE Advanced Previous Papers JEE Study Material PDF JEE Mains Mock Test JEE Advanced Mock Test JEE Daily Target

Free JEE Questions

JEE Physics Questions JEE Maths Questions JEE Chemistry Questions
banner

50,000+ JEE Students Trusted Our Score Calculator

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now
Ask AI