SOLUTION: An artist is creating tiles to use in a project. Each tile is to be in the shape of a right triangle. The shortest side of a tile is to be 4 inches long. The next shortest side

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Question 1079311: An artist is creating tiles to use in a project. Each tile is to be in the shape of a right triangle. The shortest side of a tile is to be 4 inches long. The next shortest side is to be x inches long.
Enter an expression in terms of x that models the longest side of a tile.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
The shortest side = 4
The next shortest side = x, so x > 4
The longest side, the hypotenuse, is sqrt%284%5E2%2Bx%5E2%29=sqrt%2816%2Bx%5E2%29

[That's probably all you wanted, but I'll continue]

The longest side of any triangle must be shorter than the
sum of the shorter sides, so

sqrt%2816%2Bx%5E2%29%22%22%3C%22%224%2Bx

Start with 

x%22%22%3E%22%224

Square both sides

x%5E2%22%22%3E%22%2216

Add 16 to both sides:

16%2Bx%5E2%22%22%3E%22%2216%2B16

16%2Bx%5E2%22%22%3E%22%2232

Take the positive square roots of both sides:

sqrt%2816%2Bx%5E2%29%22%22%3E%22%22sqrt%2832%29

sqrt%2816%2Bx%5E2%29%22%22%3E%22%22sqrt%2816%2A2%29

sqrt%2816%2Bx%5E2%29%22%22%3E%22%224%2Asqrt%282%29

Changing to <

4%2Asqrt%282%29%22%22%3C%22%22sqrt%2816%2Bx%5E2%29

Since sqrt%2816%2Bx%5E2%29%22%22%3C%22%224%2Bx

4%2Asqrt%282%29%22%22%3C%22%22sqrt%2816%2Bx%5E2%29%22%22%3C%22%224%2Bx 

Edwin