What radius of a circle is required to inscribe a square with an apothem of 4.95 inches?a. 5inb. 6inc. 7ind. 8inPlease explain how to get the answer, I want to know how to do this and not just be given the answer
Accepted Solution
A:
we know that The apothem goes from the center to mid-point in one of the square sides. then If the apothem is -------> 4.95 in so the length of one side of the square is 2 * 4.95--------> 9.9 in the diameter of the circle is equals to the diagonal of the square
applying the Pythagorean theorem
a²+ b²= c² a = b ---------> 9.9 in
2a² = c² c²=2 * 9.9² c²=196.02----------> c=√196.02---------- > c=14 in the diameter is 14 in so the radius r=14/2----------> r=7 in