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A helicopter landing pad has a length of 80 ft and a width of 50 ft. A safety zone of uniform width, which is not to be entered during landing, surrounds the landing pad. The landing pad and safety zone together have a combined area of 10800 ft2, what is the uniform width (safety zone) around the landing pad?

Respuesta :

ChoiSungHyun

Step-by-step explanation:

Let w be the uniform width of the safety zone.

We have combined area = 10,800ft².

=> Combined area = Length * Width

= (80 + 2w)(50 + 2w)ft².

Therefore (80 + 2w)(50 + 2w) = 10,800.

=> 4,000 + 260w + 4w² = 10,800

=> 4w² + 260w - 6,800 = 0

=> w² + 65w - 1,700 = 0

=> (w - 20)(w + 85) = 0

=> w = 20 or w = -85

(w = -85 is rejected as width must be positive)

Hence the uniform width is 20ft.

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