Question

For what value of x is PQ BC pls look at picture

Answer 1

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

Answer 2

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, $\frac{AP}{PB} = \frac{AQ}{QC}$

Putting in the values to get:

$\frac{x}{x+7} = \frac{x-3}{x+1}$

$x(x+1) = (x-3)(x+1)$

$x^2+x=x^2+7x-3x-21$

$7x-3x-x= 21$

$3x=21$

$x=7$

Therefore, the value of $x$ in this case is equal to 7.