Question

1. create a scaled copy of abcd using a scale factor of 4. 2. triangle z is a scaled copy of triangle m. select all the sets of values that could be the side lengths of triangle z. a) 8,11,and 14. b) 10,17.5,and 25. c) 6,9,and 11. d) 6,10.5,and 15. e) 8,14,and 20.

Explanation:

Step1: Recall the property of similar - scaled triangles

For two similar triangles (where one is a scaled - copy of the other), the ratios of their corresponding side lengths are equal. Let the scale factor be $k$. If the side lengths of triangle $M$ are $a = 4$, $b = 7$, and $c = 10$, and the side lengths of triangle $Z$ are $a'$, $b'$, and $c'$, then $\frac{a'}{a}=\frac{b'}{b}=\frac{c'}{c}=k$.

Step2: Check each option

Option a

For side - lengths $8,11,14$:
$\frac{8}{4}=2$, $\frac{11}{7}\approx1.57$, $\frac{14}{7} = 2$. Since the ratios are not equal, this is not a scaled - copy.

Option b

For side - lengths $10,17.5,25$:
$\frac{10}{4}=2.5$, $\frac{17.5}{7}=2.5$, $\frac{25}{10}=2.5$. Since the ratios of the corresponding side lengths are equal, this is a scaled - copy.

Option c

For side - lengths $6,9,11$:
$\frac{6}{4}=1.5$, $\frac{9}{7}\approx1.29$, $\frac{11}{10}=1.1$. Since the ratios are not equal, this is not a scaled - copy.

Option d

For side - lengths $6,10.5,15$:
$\frac{6}{4}=1.5$, $\frac{10.5}{7}=1.5$, $\frac{15}{10}=1.5$. Since the ratios of the corresponding side lengths are equal, this is a scaled - copy.

Option e

For side - lengths $8,14,20$:
$\frac{8}{4}=2$, $\frac{14}{7}=2$, $\frac{20}{10}=2$. Since the ratios of the corresponding side lengths are equal, this is a scaled - copy.

Answer:

b) $10,17.5$, and $25$;
d) $6,10.5$, and $15$;
e) $8,14$, and $20$