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620 feet of fencing is available to enclose a rectangular yard alongside of a river, which is one side of the rectangle. What dimensions will produce an area of 48,000 square feet? (Note that the fence is not needed in the side next to the river.)

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amna04352

Answer:

150 ft × 320 ft

160 ft × 300 ft

Step-by-step explanation:

Length: 620-2x

Width: x

(620-2x)x = 48000

2x² - 620x + 48000 = 0

x² - 310x + 24000 = 0

x² - 150x - 160x + 24000 = 0

x(x - 150) - 160(x - 150) = 0

(x - 160)(x - 150) = 0

x = 150, 160

For x = 150,

Length = 620-2(150) = 320

For x = 160,

Length = 620 - 2(160) = 300

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