SOLUTION: what is the area of an inscribed square whose radius is 8 inches?

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Question 203382: what is the area of an inscribed square whose radius is 8 inches?
Answer by jsmallt9(2063) About Me  (Show Source):
You can put this solution on YOUR website!
Better wording would be: What is the area of a square inscribed in a circle whose radius is 8 inches? If this is your problem then , the picture looks like:
drawing%28400%2C+400%2C+-2%2C+2%2C+-2%2C+2%2C+circle%280%2C+0%2C+sqrt%282%29%29%2C+line%28-1%2C+-1%2C+1%2C+-1%29%2C+line%281%2C+-1%2C+1%2C+1%29%2C+line%281%2C+1%2C+-1%2C+1%29%2C+line%28-1%2C+1%2C+-1%2C+-1%29%2C+line%280%2C+0%2C+1%2C+1%29%2C+line%280%2C+0%2C+1%2C+0%29%2C+locate%28.4%2C+.7%2C+8%29%2C+locate%28.2%2C+.2%2C+45%29%2C+locate%281.1%2C+.5%2C+x%29%2C+locate%28-.9%2C+0%2C+2x%29%29
Since the area of a square is the square (hence the term) of the side, we need to find the side of the square. As I hope you can see, finding the leg of the right triangle will help us find the side of the square.

In all 45-45-90 triangles the ratio of the hypotenuse to a leg is Sqrt%282%29. In the 45-45-90 right triangle shown, the hypotenuse is 8. Substituting this into the ratio we can find the leg (using x for leg because "l" can be confused with "1"): 8%2Fx+=+sqrt%282%29
Multiplying both sides by x
8+=+x%2Asqrt%282%29
Divide both sides by sqrt(2):
8%2Fsqrt%282%29+=+x
Now the leg, x, is 1/2 of the side of the square, s. So the side of the square is twice as much:
s+=+2%288%2Fsqrt%282%29%29+=+16%2Fsqrt%282%29
A+=+s%5E2+=+%2816%2Fsqrt%282%29%29%5E2+=+256%2F2+=+128 square inches.