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------------------------------------------------ Un triángulo tiene lados de longitud [tex]8 \text{ semanas} + 8x[/tex] centímetros, [tex]3 \text{ semanas} + 10 \text{ años}[/tex] centímetros, y [tex]4 \text{ años} + 8x[/tex] centímetros.

¿Qué expresión representa el perímetro, en centímetros, del triángulo?

A. [tex]13wy + 16x + 12xy + 16x + 11 \text{ semanas} + 14 \text{ años}[/tex]

B. [tex]15wy + 26xy[/tex]

C. [tex]11 \text{ semanas} + 18x + 12 \text{ años}[/tex]

To find the perimeter of the triangle, we need to sum the lengths of all three sides. The side lengths are given as:

1. [tex]\( 8 \, \text{semanas} + 8x \)[/tex]
2. [tex]\( 3 \, \text{semanas} + 10 \, \text{años} \)[/tex]
3. [tex]\( 4 \, \text{años} + 8x \)[/tex]

We will add these expressions step by step.

1. Add the constants related to "semanas" :

[tex]\( 8 \, \text{semanas} \)[/tex] and [tex]\( 3 \, \text{semanas} \)[/tex].

So, [tex]\( 8 \, \text{semanas} + 3 \, \text{semanas} = 11 \, \text{semanas} \)[/tex].

2. Add the constants related to "años" :

[tex]\( 10 \, \text{años} \)[/tex] and [tex]\( 4 \, \text{años} \)[/tex].

So, [tex]\( 10 \, \text{años} + 4 \, \text{años} = 14 \, \text{años} \)[/tex].

3. Add the terms related to "x" :

[tex]\( 8x \)[/tex] and [tex]\( 8x \)[/tex].

So, [tex]\( 8x + 8x = 16x \)[/tex].

Now, we combine these results to form the complete expression for the perimeter:

[tex]\( \text{Perimeter} = 11 \, \text{semanas} + 16x + 14 \, \text{años} \)[/tex]

This is the simplified expression representing the perimeter, in centimeters, of the triangle.