If The Area Of The Square Is 72 Inches Squared, What Is The Radius?


2 Answers

Linda Jane Profile
Linda Jane answered
I'm assuming that the  square is inscribed in a circle and that is the radius that you are looking for.
(1) S is side of the square so S^2=72 and s=sqrt(72)=8.49

(2) Draw the square. Next draw a circle around the square so that the corners of the square touch the circle.

(3) Draw a point in the center of the square

(4) Draw a line from the center of the square to the top of one side. Draw a line from the center of the square to the bottom of the same side.
(5) You now have a triangle. The two sides connected to the center are the radius and the angle at the center point is a 90 degree angle

(6) A triangle with a 90 degree angle is a right triangle and its base is a side of the square that we calculated in  (1) 8.49

(7) Now we can use the Pythagorean theorum H^2=A^2 + B^2
A and B are both radii of the circle and H = 8.49

(8) So we have 8.49^2=R^2+R^2

.(9)  72 = 2R^2

(10) 36 = R^2

(11) R=sqrt(36) = 6
Anonymous Profile
Anonymous answered

The area of a rectangle is 72 in squared.  The width of one of the sides is 8 inches.  Find the length.

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