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.

Explanation:

Step1: Recall triangle - side - length condition

For three numbers \(a\), \(b\), and \(c\) to be the side - lengths of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the set \(8,11,14\)

Let \(a = 8\), \(b = 11\), \(c = 14\).
\(8+11 = 19>14\), \(8 + 14=22>11\), \(11 + 14 = 25>8\). So, \(8\), \(11\), and \(14\) can be the side - lengths of a triangle.

Step3: Check the set \(10,17.5,25\)

Let \(a = 10\), \(b = 17.5\), \(c = 25\).
\(10+17.5 = 27.5>25\), \(10 + 25=35>17.5\), \(17.5 + 25 = 42.5>10\). So, \(10\), \(17.5\), and \(25\) can be the side - lengths of a triangle.

Answer:

a) 8, 11, and 14; b) 10, 17.5, and 25