a company is producing rectangular sheets of plastic. each has an area of (9x^2+30x+25) ft^2.. The dimensions of each sheet are of the form ax + b, where a and b are whole numbers. Find an expression for the perimeter of a sheet. Find the perimeter when x=4 ft.
9x^2+30x+25 =(3x+5)^2 It is square Perimeter= 4(3x+5) At x=4 Perimeter= 4(3*4+5)= 4(12+5)=4*17=68
Let a = 3 Let b = 5 (3x + 5)? = (3x + 5)(3x + 5) (3x + 5)(3x + 5) = 9x? + 15x + 15x + 25 9x? + 15x + 15x + 25 = 9x? + 30x + 25 The perimeter (p(x)) is: p(x) = 4(3x + 5) p(4) = 4(12 + 5) p(4) = 48 + 20 p(4) = 68
(9x^2+30x+25) = (9x^2 + 15x + 15x + 25) = 3x(3x + 5) + 5(3x + 5) = (3x + 5)(3x + 5) So the sides are 3x + 5 and 3x + 5 ft The perimeter = 3x + 5 + 3x + 5 + 3x + 5 + 3x + 5 = 12x + 20 = 4(3x + 5) ft When x = 4ft, the perimeter = 4(3(4) + 5) = 4(12 + 5) = 4(17) = 68ft
