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

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The problem states that the distance from AB equals BC, with AB defined as x^2 and BC as 9. By solving for x, it is determined that x equals 3, making AB equal to 9. Since both AB and BC are 9, the total distance AC is calculated by adding AB and BC, resulting in AC being 18. The conclusion assumes AC is a straight line; alternative configurations may require different considerations. The final answer is that AC equals 18.
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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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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