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14 Sep 2024, 12:26
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0% (00:00) correct
100% (02:33) wrong based on 2 sessions
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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
Indicate all such lengths.
A. 20
B. 30
C. 40
D. 50
E. 60
F. 70
G. 80
H. 90
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Official Answer
B,C,E,G
08 Feb 2025, 12:00
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OE
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 substitute 2,400/a for b in the equation 2a + b = 140 to get the equation \(2a+\frac{2400}{a}=140\) It follows that \(2a^2 + 2,400 = 140a,\) or \(a^2 - 70a + 1,200 = 0.\) 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 if a = 40, then \(b=\frac{2400}{30} = 80\) then \(b=\frac{2400}{40} = 60\) So the possible lengths of the sides are 30, 40, 60, and 80. Tus the correct answer consists of Choices B, C, E, and G.
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 substitute 2,400/a for b in the equation 2a + b = 140 to get the equation \(2a+\frac{2400}{a}=140\) It follows that \(2a^2 + 2,400 = 140a,\) or \(a^2 - 70a + 1,200 = 0.\) 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 if a = 40, then \(b=\frac{2400}{30} = 80\) then \(b=\frac{2400}{40} = 60\) So the possible lengths of the sides are 30, 40, 60, and 80. Tus the correct answer consists of Choices B, C, E, and G.
