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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

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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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
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