SOLUTION: Will an 18" x 13" rectangle fit inside a 21" diameter circle? I asked this question earlier and gave the wrong dimensions of 18" x 6". Sorry. Thank you very much.

Question 1020881: Will an 18" x 13" rectangle fit inside a 21" diameter circle?
I asked this question earlier and gave the wrong dimensions of 18" x 6". Sorry.
Thank you very much.
Found 3 solutions by solver91311, ikleyn, josgarithmetic:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Depends. Is ?

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let us calculate the diagonal size. It is = 22.20'' (approximately). Now answer yourself if the rectangle fits inside the circle. By the way, if a right-angled triangle is inscribed into a circle, then its hypotenuse is a diameter of the circle. See the lesson An inscribed angle in a circle, Corollary 3 and 4 in this site.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Put the centers of each at the origin of a cartesian coordinate system. The circle will be . Cut the 18 inch length in half, so it be 9 inch. Now put your attention onto quadrant 1. One coordinate on the circle would be 9; what will the other coordinate be? Will it be less than or equal to ? If yes, then the rectangle will fit. If no, then the rectangle will not fit.

Another way: Draw a diagonal of your 18 inch by 13 inch rectangle. What is the length of this diagonal? Pythagorean Theorem for Right Triangle. Is this diagonal less than or equal to 21? If yes,... then it will fit in the circle of diameter 21.
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