ExplanationYou 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 \(\frac{2400}{a}\) for b

in the equation 2a + b = 140 to get the equation \(2a + \frac{2400}{a}=140\). It follows that \(2a^2 +

2400 = 140a\), or \(a^2 - 70a + 1200 = 0\).

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

\(b = \frac{2400}{30} =80\); if a = 40, then \(b = \frac{2400}{40} =60\). 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.

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Sandy

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