SOLUTION: What is the width, in inches, of the largest rectangle with length 16 inches that can be cut from a circular piece of cardboard having a radius of 10 inches.

Algebra ->  Rectangles -> SOLUTION: What is the width, in inches, of the largest rectangle with length 16 inches that can be cut from a circular piece of cardboard having a radius of 10 inches.      Log On


   

Question 120213: What is the width, in inches, of the largest rectangle with length 16 inches that can be cut from a circular piece of cardboard having a radius of 10 inches.
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE ANSWER IS A 12 BY 16 INCH RECTANGLE. CAN'T DRAW IT OUT FOR YOU BUT:
DRAW A 10 INCH RADIUS CIRCLE.
DRAW A HORIZONTAL LINE THROUCH THE CENTER.
THIS IS A 20 INCH LINE.
NOW DRAW A 16 INCH PARALLEL LINE ABOVE & BELOW THIS LINE.
NOW DRAW A LINE FROM THE CENTER TO THE POINT WHERE THE 16 INCH LINE TOUCHES THE CIRCLE.
DROP OR RAISE A VERTICLE LINRE FROM THIS INTERSECTION POINT TO THE 20 INCH DIAMETER LINE.
YOU NOW HAVE A RIGHT TRIANGLE WITH DIMENTIONS OF 10 INCHES FOR THE HYPOTENUSE & 8 INCHES FROM THE CENTER TO THR PERPENDICULAR LINE JUST DRAWN.
THIS FORMS A 6-8-10 TRIANGLE. THUS THE WIDTH OF THE RECTANGLE IS 2*6=12 INCHES.
THEREFORE THE WIDTH OF THE RECTANGLE IS 12.