Question

1. 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 - triangles

For two similar triangles (triangle M and triangle Z, where Z is a scaled - copy of M), the ratios of corresponding side lengths are equal. Let the side lengths of triangle M be \(a = 7\), \(b = 4\), \(c = 10\). The ratios of side - lengths in similar triangles should be the same. We can check the ratios of the given sets of numbers to see if they are in proportion to \(7:4:10\).

Step2: Check option a

For the set \(8,11,14\), \(\frac{8}{7}
eq\frac{11}{4}
eq\frac{14}{10}\), so this set does not represent the side - lengths of a scaled copy of triangle M.

Step3: Check option b

For the set \(10,17.5,25\), \(\frac{10}{7}=\frac{10\div1}{7\div1}=\frac{10}{7}\), \(\frac{17.5}{4}=\frac{17.5\div0.5}{4\div0.5}=\frac{35}{8}
eq\frac{10}{7}\), so this set does not represent the side - lengths of a scaled copy of triangle M.

Step4: Check option c

For the set \(6,9,11\), \(\frac{6}{7}
eq\frac{9}{4}
eq\frac{11}{10}\), so this set does not represent the side - lengths of a scaled copy of triangle M.

Step5: Check option d

For the set \(6,10.5,15\), \(\frac{6}{4}=\frac{6\div2}{4\div2}=\frac{3}{2}\), \(\frac{10.5}{7}=\frac{10.5\div0.5}{7\div0.5}=\frac{21}{14}=\frac{3}{2}\), \(\frac{15}{10}=\frac{15\div5}{10\div5}=\frac{3}{2}\). The ratios of the side - lengths are equal, so this set could be the side - lengths of a scaled copy of triangle M.

Step6: Check option e

For the set \(8,14,20\), \(\frac{8}{4} = 2\), \(\frac{14}{7}=2\), \(\frac{20}{10}=2\). The ratios of the side - lengths are equal, so this set could be the side - lengths of a scaled copy of triangle M.

Answer:

d. \(6,10.5,15\)
e. \(8,14,20\)