Question

For what value of x is P|| BC? A. 5 B. 6 C. 7 D. 8

Answer 1

Answer:

Option C. x=7

Step-by-step explanation:

we know that

If PQ is parallel to BC

then

triangles APQ and ABC are similar

Remember that

If two figures are similar them the ratio of its corresponding sides is proportional

so

$\frac{AP}{AB}=\frac{AQ}{AC}$

substitute the values

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

Solve for x

$\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units$