Question

find the value of x in the triangle abc a=(x+8) b=(3x-1) c=(x-3)
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Answer 1

Answer:

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that AD=4x−38, BD=3x−1, AE=8x−7 and CE=5x−3. Let AC=x

Using the basic proportionality theorem, we have

BD

AD

​  

=  

AC

AE

​  

 

⇒  

3x−1

4x−3

​  

=  

x

8x−5

​  

 

⇒x(4x−3)=(3x−1)(8x−5)

⇒4x  

2

−3x=3x(8x−5)−1(8x−5)

⇒4x  

2

−3x=24x  

2

−15x−8x+5

⇒4x  

2

−3x=24x  

2

−23x+5

⇒24x  

2

−23x+5−4x  

2

+3x=0

⇒20x  

2

−20x+5=0

⇒5(4x  

2

−4x+1)=0

⇒4x  

2

−4x+1=0

⇒(2x)  

2

−(2×2x×1)x+1  

2

=0(∵(a−b)  

2

=a  

2

+b  

2

−2ab)

⇒(2x−1)  

2

=0

⇒(2x−1)=0

⇒2x=1

⇒x=  

2

1

​  

 

Hence, x=  

2

1

​  

.