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Question

A round table has radius 4. Six rectangular place mats are placed on the table. Each place mat has width 1 and length x as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length x. Further, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. What is x? FIGURE

Accepted Answer

FIGURE Notice that AE is 16 the circumference of the circle. Therefore, AE is the side length of an inscribed hexagon with side length 4. AFE is a right triangle with AF=12. The length of EF=x+32. Using the Pythagorean Theorem, we get 4^2 = (12)^2 + (x+32)^2 Solving for x, we get x = 37-32 37-32