Question
The sides of a triangle measure 3 Square root 6, 2 Square root 24, and 7 square root 54. What is the perimeter of the triangle?
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Answer
what is the answer
Answered by
GPT 3.5
To simplify the given side lengths, we can factor out perfect squares from the square root terms.
The side lengths can be rewritten as:
3 sqrt(6) = 3 * sqrt(2 * 3) = 3 * sqrt(2) * sqrt(3) = 3sqrt(2 * sqrt(3))
2 sqrt(24) = 2 * sqrt(4 * 6) = 2 * sqrt(2^2 * 6) = 2 * 2 * sqrt(6) = 4 sqrt(6)
7 sqrt(54) = 7 * sqrt(9 * 6) = 7 * sqrt(3^2 * 6) = 7 * 3 * sqrt(6) = 21 sqrt(6)
Now, we can express the perimeter of the triangle by adding up all three side lengths:
Perimeter = 3 sqrt(2 sqrt(3)) + 4 sqrt(6) + 21 sqrt(6)
Combining like terms, we have:
Perimeter = 3 sqrt(2 sqrt(3)) + (4 + 21) sqrt(6)
= 3 sqrt(2 sqrt(3)) + 25 sqrt(6)
Therefore, the perimeter of the triangle is 3 sqrt(2 sqrt(3)) + 25 sqrt(6).
The side lengths can be rewritten as:
3 sqrt(6) = 3 * sqrt(2 * 3) = 3 * sqrt(2) * sqrt(3) = 3sqrt(2 * sqrt(3))
2 sqrt(24) = 2 * sqrt(4 * 6) = 2 * sqrt(2^2 * 6) = 2 * 2 * sqrt(6) = 4 sqrt(6)
7 sqrt(54) = 7 * sqrt(9 * 6) = 7 * sqrt(3^2 * 6) = 7 * 3 * sqrt(6) = 21 sqrt(6)
Now, we can express the perimeter of the triangle by adding up all three side lengths:
Perimeter = 3 sqrt(2 sqrt(3)) + 4 sqrt(6) + 21 sqrt(6)
Combining like terms, we have:
Perimeter = 3 sqrt(2 sqrt(3)) + (4 + 21) sqrt(6)
= 3 sqrt(2 sqrt(3)) + 25 sqrt(6)
Therefore, the perimeter of the triangle is 3 sqrt(2 sqrt(3)) + 25 sqrt(6).
Answered by
GPT 3.5
The perimeter of the triangle is 3 sqrt(2 sqrt(3)) + 25 sqrt(6).
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