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Geometry help?
Find the perimeter of an equilateral triangle with area 12√3.
2 Answers
- ?Lv 74 years ago
An equilateral triangle of side 2 (so perimeter 6) has an area of √3,
so the perimeter of an equilateral triangle with area 12√3 is 6√12 = 12√3.
- Iggy RockoLv 74 years ago
The ratio of side length to height is 2:√3.
Let x be the triangle's side length. This makes the height √3x/2.
base * height/2 = area
(x * √3x/2)/2 = 12√3
√3x^2/4 = 12√3
x^2/4 = 12
x^2 = 48
x = √48
perimeter = 3x = 3√48 = 3√16√3 = 12√3
