题目信息
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)
A:5 ft 6 in
B:5 ft 
in
in
C:5 ft 3 in
D:5 ft
E:4 ft 9 in
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正确答案：
C:5 ft 3 in
Geometry Rectangles; Triangles
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 ΔAFG 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.
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 ΔAFG 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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