Question

klmn \sim fghj. use the diagram below to answer the following questions.

a) find the scale factor from klmn to fghj.

b) find the scale factor from fghj to klmn.

c) find the value of x.

Explanation:

Identificar lados correspondientes

Using the Lados correspondientes knowledge point

$$ KLMN \sim FGHJ \implies \frac{FG}{KL} = \frac{GH}{LM} = \frac{HJ}{MN} = \frac{JF}{NK} $$

$$ KL = 30,\quad JF = 14 $$

Calcular el factor de escala de KLMN a FGHJ

Using the Semejanza de polígonos knowledge point

$$ k_{1} = \frac{JF}{KL} = \frac{14}{30} = \frac{7}{15} $$

Calcular el factor de escala de FGHJ a KLMN

Using the Semejanza de polígonos knowledge point

$$ k_{2} = \frac{KL}{JF} = \frac{30}{14} = \frac{15}{7} $$

Calcular el valor de x

Using the Lados correspondientes and Semejanza de polígonos knowledge points

$$ \frac{FG}{KL} = \frac{7}{15} \implies \frac{x}{30} = \frac{7}{15} $$

$$ x = 30 \cdot \frac{7}{15} = 14 $$

Answer:

Question a

El factor de escala de \(KLMN\) a \(FGHJ\) es \(\frac{7}{15}\).

Question b

El factor de escala de \(FGHJ\) a \(KLMN\) es \(\frac{15}{7}\).

Question c

\(x = 14\)