0

Guest

Courses New

If A (6,3) ,B(-3,5) ,C(4,-2) and D(x,3x) are four points If the ratio of area of triangle DBC and triangle ABC is 1:2 then value of x will be

If A (6,3) ,B(-3,5) ,C(4,-2) and D(x,3x) are four points If the ratio of area of triangle DBC and triangle ABC is 1:2 then value of x will be

Grade:12

3 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear pallvi

Find the area of triangle ABC

ΔABC =49/2


similerly find the area of triangle DBC

ΔDBC =7|2x-1|

now given ΔDBC/ΔABC   =1/2

  so   7|2x-1|/49/2  = 1/2

       2 |2x-1|/7 =1/2

         |2x-1| =7/4

      2x-1  =±7/4


+ve sign                                             -ve sign


2x-1 = 7/4                                        2x-1 =-7/4

x =11/8                                            x=-3/8


Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed  solution very  quickly.

 We are all IITians and here to help you in your IIT JEE preparation.

All the best.
 
Regards,
Askiitians Experts
Badiuddin

madhuri
11 Points
6 years ago
in triangle PQR and triangleDEF ,angle P=angleE=30degrees,PQ/DE=PR/EF and angle F=75degrees show that PQ=PR
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to the question.
 
The area of triangle with vertices: (x1, y1), (x2, y2), (x3, y3) is
A = ½ | x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2) |
 
Using this we get the area of ΔABC = 49/2
 
similarly, we find the area of triangle DBC
ΔDBC =7|2x-1|
 
now given ΔDBC/ΔABC   = 1/2
7|2x – 1|/(49/2)  = 1/2
2 |2x – 1|/7 =1/2
|2x – 1| = 7/4
2x – 1 = ±7/4
 
Hence, x = 11/8 or –3/8
 
Thanks and regards,
Kushagra

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