Question

If 3a+5abc-3c=6d
find 'a' when b=5,c= -2, and d=4
please full explanation!
and please fast!!!

Answer 1

Answer:

Given,

A(6,3),B(−3,5),C(4,−2)andD(x,3x)

By using area of triangle =  

2

1

​  

∣x  

1

​  

(y  

2

​  

−y  

3

​  

)+x  

2

​  

(y  

3

​  

−y  

2

​  

)+x  

3

​  

(y  

1

​  

−y  

2

​  

)∣

Area of  ΔDBC =  

∣

∣

∣

∣

∣

​  

 

2

(x)(5+2)+(−3)(−2−3x)+4(3x−5)

​  

 

∣

∣

∣

∣

∣

​  

=  

∣

∣

∣

∣

∣

​  

 

2

7x+6+9x+12x−20

​  

 

∣

∣

∣

∣

∣

​  

=  

∣

∣

∣

∣

∣

​  

 

2

28x−14

​  

 

∣

∣

∣

∣

∣

​  

 

Area of ΔABC =  

∣

∣

∣

∣

∣

​  

 

2

(6)(5+2)+(−3)(−2−3)+4(3−5)

​  

 

∣

∣

∣

∣

∣

​  

=  

∣

∣

∣

∣

∣

​  

 

2

42+15−8

​  

 

∣

∣

∣

∣

∣

​  

=  

2

49

​  

 

Given:  

AreaofABC

AreaofDBC

​  

=  

2

1

​  

 

2

49

​  

 

∣

∣

∣

∣

∣

​  

 

2

28x−14

​  

 

∣

∣

∣

∣

∣

​  

 

​  

=  

2

1

​  

 

∣28x14∣=  

2

49

​  

 

28x14=±  

2

49

​  

 

Taking a positive sign

28x14=  

2

49

​  

 

56x−28=49

56x=77

x=  

56

77

​  

=  

8

11

​  

 

Taking a negative sign

28x14=−  

2

49

​  

 

56x−28=−49

56x=−21

x=  

56

21

​  

=  

8

3

​  

 

So, x=  

8

11

​  

 or x=  

8

3

​