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A piece of paper is 12cm long and 9 cm wide . along itsfour sides of the paper is cut to become x wide ribbon , in order taht the reminder of paper area 54

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Area of rectangular piece of paper = 12 * 9 = 108 cm² a piece of width x cm is cut out from all sides of rectangle.. Width of the remaining piece of paper = 9 - 2 x cm length of the remaining piece of paper = 12 - 2 x cm

The area of the remaining piece = (9 - 2x ) (12 - 2x) cm² = 108 - 42 x + 4 x² = 54 cm² => 2 x² - 21 x +27 = 0 factors of 2 * 27 = 2, 3, 6, 9, 18, 27, 54 , 1 -18 - 3 sum to -21 (2 x - 3 )(x - 9) = 0 => x = 1.5 cm or 9 cm x cannot be 9 cm. Hence x = 1.5 cm.

Area of rectangular piece of paper = 12 * 9 = 108 cm² a piece of width x cm is cut out from all sides of rectangle.. Width of the remaining piece of paper = 9 - 2 x cm length of the remaining piece of paper = 12 - 2 x cm

The area of the remaining piece = (9 - 2x ) (12 - 2x) cm² = 108 - 42 x + 4 x² = 54 cm² => 2 x² - 21 x +27 = 0 factors of 2 * 27 = 2, 3, 6, 9, 18, 27, 54 , 1 -18 - 3 sum to -21 (2 x - 3 )(x - 9) = 0 => x = 1.5 cm or 9 cm