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

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In summary, the notation "AB = x^2" in the given problem means that the length of side AB is equal to x squared. To find the length of side AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (side AC) is equal to the sum of the squares of the other two sides (AB and BC). This triangle is a right triangle because it satisfies the Pythagorean theorem. The length of a side cannot be negative, so the length of side AB cannot be negative in this problem. Any positive value for x can be used to find the length of side AC, but it will affect the length of side AB.
  • #1
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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  • #2
If AB = BC and BC = 9 then AB = 9. AB + BC = AC = 9 + 9 = 18.
 
  • #3
greg1313 said:
If AB = BC and BC = 9 then AB = 9. AB + BC = AC = 9 + 9 = 18.

It feels good to be right.
 
  • #4
That is assuming AC is a straight line, of course. If not, how do we answer?
 

1. What does "AB = x^2" mean in the given problem?

The notation "AB = x^2" means that the length of side AB is equal to x squared.

2. How do we find the length of side AC?

To find the length of side AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (side AC) is equal to the sum of the squares of the other two sides (AB and BC). So, AC^2 = AB^2 + BC^2. Since we know the values of AB and BC, we can substitute them into the equation and solve for AC.

3. Is this a right triangle?

Yes, it is a right triangle because it satisfies the Pythagorean theorem, as stated in the previous answer.

4. Can the length of side AB be negative?

No, the length of a side cannot be negative. In this problem, since the length of a side is represented by x squared, it must be a positive value.

5. Can we use any value for x to find the length of side AC?

Yes, we can use any value for x as long as it is a positive number. However, keep in mind that the value of x will determine the length of side AB, which in turn will affect the length of side AC.

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