Question

In triangle ,A-P-B, A-Q-C and line segment PQ is parallel to line segment BC.If AP =8x-7,PB =5x-3,AQ =4x-3 and QC=3x-1, find the value of x.
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Answer 1

Answer:

According to equation,

DE∥BC

∴

BD

AD

=

CE

AE

(By B.P. Theorem)

or,

3x−1

4x−3

=

5x−3

8x−7

or, 24x

2

−29x+7=20x

2

−27x+9

or, 4x

2

−2x−2=0

or, 2x

2

−x−1=0

Again, 2x

2

−x−1=0

or, 2x

2

−2x+1=0

or, 2x(x−1)+1(x−1)=0

or, (2x+1)(x−1)=0

∴x=−

2

1

,1

Hence obtion (D) is correct answer