SOLUTION: what size rectangle will fit inside a circle of radius 30 feet if the lenght of the rectangle must be three ties it is width

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Question 724247: what size rectangle will fit inside a circle of radius 30 feet if the lenght of the rectangle must be three ties it is width
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

If you recall that a 90%5Eo angle inscribed in a circle intercepts an arc measuring 180%5Eo, you realize that the diagonals of the rectangle are diameters of the circle, so they measure 60feet.
Each diagonal divides the rectangle into two congruent right triangles with sides measuring x feet and 3xfeet.
According to the Pythagorean theorem,
x%5E2%2B%283x%29%5E2=60%5E2 --> x%5E2%2B9x%5E2=3600 --> 10x%5E2=3600 --> x=sqrt%28360%29 --> x=sqrt%2836%2A100%29 --> x=sqrt%2836%29%2Asqrt%2810%29 --> x=6sqrt%2810%29
SO the sides of the rectangle measure
highlight%286sqrt%2810%29%29feet and highlight%2818sqrt%2810%29%29feet.