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Here, \( a = 1, b = 1, c = -10100 \).Calculate the discriminant: \( 1^2 - 4 imes 1 imes (-10100) = 1 + 40400 = 40401 \).The square root of 40401 is 201.Calculate \( n \): \( n = rac{-1 \pm 201}{2} \).Choose the positive solution: \( n = rac{200}{2} = 100 \).A rectangle has a length that is 3 times its width. If the perimeter is 48 meters, find the area of the rectangle.The perimeter formula is \( 2( ext{length} + ext{width}) = 48 \).Substitute: \( 2(3w + w) = 48 \), so \( 8w = 48 \).The length is \( 3 imes 6 = 18 \).Calculate the area: \( 18 imes 6 = 108 \).