Overlapping Frames

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A wooden frame 1 foot wide has been constructed around each of two rectangular sheets of glass measuring 4 feet by 5 feet. If the area of overlapping glass in the figure above measures 1 foot by 2 feet, what fraction of the total area of the glass sheets and wooden frames is overlapping?

Review: Overlapping Frames


Explanation

In this question, the overlapping area of glass plus frame is the white rectangle in the middle with the black border around that white rectangle. However, some portion of the frame is overlapping, making that part confusing. Let's just consider the overlapping portion of the lower left window-plus-frame. Let's ignore the distinction between frame and non-frame and focus on total area. In that case, the entire lower left window-plus-frame is a rectangle measuring . We have to add the two along each dimenion, since it's on both sides in each dimension. And the smaller rectangle, the portion of overlap, measures . The fraction of one rectangle that overlaps is , and this stays the same when we add an identical rectangle of equal overlap. Therefore the correct answer is .

The correct answer is (C).


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