# SOLUTION: The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?

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 Question 348138: The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle?Answer by nerdybill(6958)   (Show Source): You can put this solution on YOUR website!The area of a rectangle is 30 square centimeters and its perimeter is 26 centimeters. What is the length and width of the rectangle? Let x = width and y = length . From:"The area of a rectangle is 30 square centimeters" (equation 1) xy = 30 . From: "perimeter is 26 centimeters" (equation 2) 26=2(x+y) . Solve equation 2 for y: 26=2(x+y) 13=x+y 13-x = y . Substitute above into equation 1 and solve for x: xy = 30 x(13-x) = 30 13x-x^2 = 30 0 = x^2-13x+30 0 = (x-15)(x+2) x = {-2, 15} We can toss out the negative solution leaving x = 15 centimeters . Substitute above into equation 1 and solve for y: xy = 30 15y = 30 y = 2 centimeters . Dimensions of rectangle: 2 by 15 centimeters