jmc

Rectangle $ABCD$ is inscribed in triangle $EFG$ such that side $AD$ of the rectangle is on side $EG$ of the triangle, as shown. The triangle's altitude from $F$ to side $EG$ is 7 inches, and $EG=10\text{ inches}$. The length of segment $AB$ is equal to half the length of segment $AD$. What is the area of rectangle $ABCD$? Express your answer as a common fraction.