Given:
A : B : C = 1 : 1 : 4
Let the angles be x, x and 4x.
x + x + 4x = 180°
6x = 180°
x = 30°
Therefore, the angles are:
30°, 30°, 120°
Since two angles are equal, the triangle is isosceles. Let the equal sides be a and the longest side be 3.
By the Cosine Rule:
3² = a² + a² − 2a² cos 120°
9 = 2a² + a²
9 = 3a²
a = √3
Perimeter = 3 + √3 + √3
= 3 + 2√3
Answer = 3 + 2√3 units
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