Respuesta :

Let us assume PQ || BC.
Then, by Basic Proportionality Theorem, we get,
AP/PB = AQ/QC
=> x/(x+7) = (x-3)/(x+1)
=> x (x+1) = (x+7)(x-3)
=> x^2 + x = x^2 - 3x + 7x - 21
=> x = 4x - 21
=> -4x + x = -21
=> -3x = -21
=> 3x = 21
=> x = 21/3
=> x = 7
Therefore, for PQ||BC the value of x should be 7
alinakincsem

Answer:

x = 7

Step-by-step explanation:

According to the proportionality theorem of triangles, if a line parallel to one side of a triangle intersects the rest of the two sides, then the line divides these two sides proportionally.

So, [tex]\frac{AP}{PB} = \frac{AQ}{QC}[/tex]

Putting in the values to get:

[tex]\frac{x}{x+7} = \frac{x-3}{x+1}[/tex]

[tex]x(x+1) = (x-3)(x+1)[/tex]

[tex]x^2+x=x^2+7x-3x-21[/tex]

[tex]7x-3x-x= 21[/tex]

[tex]3x=21[/tex]

[tex]x=7[/tex]

Therefore, the value of [tex]x[/tex] in this case is equal to 7.

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