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1998 AMC 12 Question 8

AMC12 · 1998 AMC 12

Question 8

A square with sides of length $1$ is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the center of the square with points on three of the sides, as shown. Find $x,$ the length of the longer parallel side of each trapezoid.

Question illustration
  1. $\frac35$
  2. $\frac23$
  3. $\frac34$
  4. $\frac56$
  5. $\frac78$