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  3. The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at poin

The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at poin

admin2022-10-18  80
问题
The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A，B，and C，as indicated．If X=45．what is the length AB?
(1 foot=12 inches)
选项 A、5 ft 6 in
B、
C、5 ft 3 in
D、5 ft
E、4 ft 9 in
答案C
解析
The figure above shows the left side of the rectangular board with points E, F, G, and H added and segment added. We are to determine the value of AB, which equals the value of FH. Since △AFG is an isosceles triangle, it follows that FG=FA = 0.5 ft. Moreover, EF= GH because the four pieces of the rectangular board have the same dimensions. Therefore, since EH is half the length of the 20 ft board, EH= 10 ft and we have EF+FG+GH= 10 ft, or 2(GH) + 0.5 ft = 10 ft, or GH= 4.75 ft. Hence, AB = FH= FG + GH= 0.5 ft + 4.75 ft = 5.25 ft, which equals 5 ft 3 in.
The correct answer is C.
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