Question

What is the value of x, given that PQ || BC? A. 10 B. 5 C. 7 D. 8

Answer 1

Answer:

Option B $x=5\ units$

Step-by-step explanation:

we know that

If PQ || BC, then triangles APQ and ABC are similar

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal

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

substitute the values

$\frac{9}{18+9}=\frac{x}{10+x}$

solve for x

$\frac{9}{27}=\frac{x}{10+x}\\ \\90+9x=27x\\ \\27x-9x=90\\ \\18x=90\\ \\x=5\ units$