Question

triangle z is a scaled copy of triangle m. select all sets of values that could be the side lengths of triangle z. 8, 11, and 14 10, 17.5, and 25 6, 9, and 11 6, 10.5, and 15 8, 14, and 20 triangle m 4 7 10

Explanation:

Step1: Find the scale - factor concept

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

Step2: Check each option

Option 1: For 8, 11, and 14

$\frac{8}{4}=2$, $\frac{11}{7}\approx1.57$, $\frac{14}{10}=1.4$. Since $\frac{8}{4}
eq\frac{11}{7}
eq\frac{14}{10}$, this is not a valid set.

Option 2: For 10, 17.5, and 25

$\frac{10}{4}=2.5$, $\frac{17.5}{7}=2.5$, $\frac{25}{10}=2.5$. Since $\frac{10}{4}=\frac{17.5}{7}=\frac{25}{10}=2.5$, this is a valid set.

Option 3: For 6, 9, and 11

$\frac{6}{4}=1.5$, $\frac{9}{7}\approx1.29$, $\frac{11}{10}=1.1$. Since $\frac{6}{4}
eq\frac{9}{7}
eq\frac{11}{10}$, this is not a valid set.

Option 4: For 6, 10.5, and 15

$\frac{6}{4}=1.5$, $\frac{10.5}{7}=1.5$, $\frac{15}{10}=1.5$. Since $\frac{6}{4}=\frac{10.5}{7}=\frac{15}{10}=1.5$, this is a valid set.

Option 5: For 8, 14, and 20

$\frac{8}{4}=2$, $\frac{14}{7}=2$, $\frac{20}{10}=2$. Since $\frac{8}{4}=\frac{14}{7}=\frac{20}{10}=2$, this is a valid set.

Answer:

10, 17.5, and 25; 6, 10.5, and 15; 8, 14, and 20