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  3. A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the f

A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the f

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问题 A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the fourth side. If the entire length of the fence is 140 feet, which of the following could be the length, in feet, of one of the sides of the flower bed?
Indicate all such lengths.
A 20
B 30
C 40
D 50
E 60
F 70
G 80
H 90
选项
答案B，C，E
解析 You know that the area of the rectangular flower bed is 2,400 square feet. So if the flower bed is a feet long and b feet wide, then ab = 2,400. If the side of the flower bed that is bordered by the walkway is one of the sides that are b feet long, then the total length of the three sides of the flower bed bordered by the fence is 2a + b feet. Since you are given that the total length of the fence is 140 feet, it follows that 2a + b = 140. Since ab = 2,400, you can substitutefor b in the equation 2a + b=140 to get the equation 2a += 140. It follows that 2a2 + 2,400 = 140a, or a2 - 70a + 1,200 = 0.
When you solve this equation for a(either by factoring or by using the quadratic formula), you get a = 30 or a = 40. If a = 30, then b == 80; if a = 40, then b == 60. So the possible lengths of the sides are 30, 40, 60, and 80. Thus the correct answer consists of Choices B, C, E, and G.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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