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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
147 Points
11 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


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madhuri
11 Points
3 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 629 Points
9 months 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

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