The distance from AB = BC. AB = x^2 and BC = 9. Find AC.

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Discussion Overview

The discussion revolves around finding the distance AC given that the distances AB and BC are equal, with specific values assigned to them. The context includes basic geometric reasoning and the implications of the arrangement of points A, B, and C.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant states that if AB = x^2 and BC = 9, then by finding the square root, x is determined to be 3, leading to AB being 9 and thus AC being 18.
  • Another participant agrees with the calculation that if AB = BC and both equal 9, then AC is also 18.
  • A third participant reiterates the previous point, expressing satisfaction with the correctness of their understanding.
  • One participant introduces a condition by questioning whether AC is a straight line, suggesting that the answer may differ if the arrangement is not linear.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of AC being 18 based on the given conditions, but there is a disagreement regarding the assumption of AC being a straight line, which remains unresolved.

Contextual Notes

The discussion does not clarify the geometric arrangement of points A, B, and C, which could affect the interpretation of the distances involved.

mathdad
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Find Distance AC.

The distance from AB = BC. AB = x^2 and BC = 9. Find AC.

My Work:

A------x^2------B-----9----C

sqrt{x^2} = sqrt{9}

x = 3

Then x^2 = 3^2 = 9

If AB = 9 and BC = 9, then we add AB + BC to get the entire distance. This is basic geometry.

AC = 18

Correct?
 
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If AB = BC and BC = 9 then AB = 9. AB + BC = AC = 9 + 9 = 18.
 
greg1313 said:
If AB = BC and BC = 9 then AB = 9. AB + BC = AC = 9 + 9 = 18.

It feels good to be right.
 
That is assuming AC is a straight line, of course. If not, how do we answer?
 

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