Respuesta :

calculista

Answer:

Option B [tex]x=5\ units[/tex]

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

[tex]\frac{AP}{AB}=\frac{AQ}{AC}[/tex]

substitute the values

[tex]\frac{9}{18+9}=\frac{x}{10+x}[/tex]

solve for x

[tex]\frac{9}{27}=\frac{x}{10+x}\\ \\90+9x=27x\\ \\27x-9x=90\\ \\18x=90\\ \\x=5\ units[/tex]

Similar triangles sides are in ratio. The length of the line AQ or the value of x is 5 units.

What are Similar triangles?

Two figures are known as similar triangles there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol '~'.

We know that in ΔAPQ  and ΔABC, the side PQ || BC, while the other two sides are the same sides of the triangle which means,

[tex]\overline{AP} \sim \overline{AB}[/tex]

[tex]\overline{AQ}\sim \overline{AC}[/tex]

therefore, using the SSS(Side-Side-Side) property we can say that the two triangles are similar triangles.

As discussed that the two triangles are equal, therefore, their sides will be in the same ratio.

[tex]\dfrac{AP}{AB} = \dfrac{AQ}{AC}[/tex]

[tex]\dfrac{9}{18+9} = \dfrac{x}{x+10}\\\\\dfrac{9}{27} = \dfrac{x}{x+10}\\\\9x+90 = 27x\\90=27x-9x\\90=18x\\x = 5[/tex]

Hence, the length of the line AQ or the value of x is 5 units.

Learn more about Similar triangles:

https://brainly.com/question/25882965

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