Question

the composition of transformations ( r_{y = - 5}circ r_{(90^{circ},a)} ) maps ( \triangle abc ) to ( \triangle xyz ). if the perimeter of ( \triangle xyz ) is 26, what is a possible set of values of ab, bc, and ac? explain. reflections and rotations preserve length. the perimeter of ( \triangle abc ) is equal to the perimeter of ( \triangle xyz ). the perimeter of ( \triangle abc ) is 26. a possible set of values of ab, bc, and ac is (type a whole number.)

Explanation:

Step1: Check triangle inequality

For a set of side lengths \(a\), \(b\), \(c\) to form a triangle, the following inequalities must hold: \(a + b>c\), \(a + c>b\), \(b + c>a\)

Option 1: \(a = 7\), \(b = 9\), \(c = 10\)

• \(7+9 = 16>10\)
• \(7 + 10=17>9\)
• \(9+10 = 19>7\)
• And \(7 + 9+10=26\)

Option 2: \(a = 8\), \(b = 9\), \(c = 10\)

• \(8+9=17>10\)
• \(8 + 10=18>9\)
• \(9+10=19>8\)
• But \(8 + 9+10=27

eq26\)

Option 3: \(a = 8\), \(b = 9\), \(c = 13\)

• \(8+9=17>13\)
• \(8 + 13=21>9\)
• \(9+13=22>8\)
• But \(8 + 9+13=30

eq26\)

Option 4: \(a = 15\), \(b = 17\), \(c = 20\)

• \(15+17=32>20\)
• \(15 + 20=35>17\)
• \(17+20=37>15\)
• But \(15+17 + 20=52

eq26\)

Answer:

\(7\), \(9\), and \(10\)