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In triangle ABC, DE is parllel to BC. If AD=4x-3, BD=3x-1 , AE=8x-7 and Bc=5x-3 ,then find the values of x

In triangle ABC, DE is parllel to BC. If AD=4x-3, BD=3x-1 , AE=8x-7 and Bc=5x-3 ,then find the values of x

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
Please find the answer to your question below
GivenAD=4x-3, BD=3x-1 , AE=8x-7 and EC=5x-3
SinceDE is parllel to BC,by basic proportionality theorem
(AD/DB)=(AE/EC)
(4x-3/3x-1)=(8x-7/5x-3)
By cross multiplication we get
20x2-27x+9=24x2-29x+7
2x2-x-1=0
2x2-2x+x-1=0
2x(x-1)+1(x-1)=0
(2x+1)(x-1)=0
so x=-1/2,1

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