Question

in triangle abc pq parallel to bc and ap = x, pb = x + 2, aq=x+ 3 and qc = 3x + 1 .
find x please answer me fast

Answer 1

In triangle ABC,

PQ ║ BC,

Such that, P∈ AB and Q ∈ AC,

Also, AP = 3x-19, PB = x-5, AQ = x-3, QC = 3 cm

To find : The value of x.

Since, PQ ║ BC

By the alternative interior angle theorem,

Also

By AAA similarity postulate,

Since, the corresponding sides of the similar triangle are in same proportion,

AB

AP

=

AC

AQ

AP+PB

AP

=

AQ+QC

AQ

3x−19+x−5

3x−19

=

x−3+3

x−3

2x−24

3x−19

=

x

x−3

2

−19x=4x

2

−24x−12x+72

2

−17x+72=0

By solving this,

We get, x = 8 or 9.

Hence, The value of x is 8 or 9.

Answer 2

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