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For the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
As given in the question,
For the given rectangular playpen,
Perimeter of rectangular playpen is equal to 150 feet .
Area of the rectangular playpen is equal to at least 1,000 squared feet .
Area = length × width
Let x be the length of the rectangular playpen .
Then its width is equal to 1000 / x.
Substitute the value of length and width in perimeter we get,
Perimeter of rectangular playpen = 2 ( length + width )
⇒ 150 = 2 [ x + (1,000/x)]
⇒ 150 / 2 = ( x² + 1,000 ) / x
⇒ x² + 1000 = 75x
⇒ x² -75x + 1,000 =0
Simplify quadratic equation using discriminant we get,
x = [ -( -75) ± √(-75)² - 4(1) (1,000) ] / 2(1)
⇒ x = ( 75 ± √5625 - 4000) /2
⇒ x = (75 ± 40.31) / 2
⇒ x = 57.66 or 17.35
Therefore, for the given rectangular playpen, the perimeter of rectangular playpen is 150 feet and its area is at least 1000 square feet. then the length of the rectangular playpen is equal to at least 17.35 feet and at most 57.66 feet.
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