0

Guest

Courses New

The triangle ABC,right-angled at C,has median AD.BE and CF. AD lies along the line y=x+3,BE lies along the line y=2x+4. If the length of of the hypotenuse is 60 find the area of the triangle ABC.

The triangle ABC,right-angled at C,has median AD.BE and CF. AD lies along the line y=x+3,BE lies along the line y=2x+4. If the length  of of the hypotenuse is 60 find the area of the triangle ABC.

Grade:12

1 Answers

ashutosh kataria
16 Points
6 years ago
The easiest way to solve this question is by shifting the centroid to origin.
Thus now equations of median are y=x and y=2x.
Now the coordiantes of A can be taken as (a,a) and that of B can be taken as (b,2b) 
Using centroid formula C(-a-b,-a,-2b)
Equate hypotenuse length equal to 60 get one equation. Second equation comes from slope of AC and BC product is -1.Solving both the equations you will get ab=(-800/3).
Find out area of triangle using all three co-ordinates. Area=3/2 (ab)
=400
 

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More