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