Just sum the sides ( the definition of perimeter) 9a + 292.
Perimeter = 9a + 292. Suppose 5a + 20 is the base. Then a + 196 = 3a + 76 120 = 2a 60 = a Suppose 3a + 76 is the base.
Then 5a + 20 = a + 196 4a = 176 a = 44 Suppose a + 196 is the base. Then 5a + 20 = 3a + 76 2a = 56 a = 28 So the first way gives the biggest a; use that to get the biggest perimeter.
When a triangle is isosceles, that means 2 of its sides are equal. That leaves 3 possibilities. 1) 5a + 20 = a + 196 4a = 176 a = 44 P = 5(44) + 20 + (44) + 196 + 3(44) + 76 P = 220 + 20 + 44 + 196 + 132 + 76 P = 688 units 2) 5a + 20 = 3a + 76 2a = 56 a = 28 P = 5(28) + 20 + (28) + 196 + 3(28) + 76 P = 140 + 20 + 28 + 196 + 84 + 76 P = 544 units 3) a + 196 = 3a + 76 2a = 120 a = 60 P = 5(60) + 20 + (60) + 196 + 3(60) + 76 P = 300 + 20 + 60 + 196 + 180 + 76 P = 832 units Of the 3 possibilities, the greatest possible perimeter is 832 units.
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