rectangle shape has an area of (4x to the second power + 12x +9) ft to the second power the dimensions are of the form cx +d, where c and d are whole numbers.

Question

Find an expression for the perimeter of the shape. Find the perimeter when x=2ft

detrermine whether it is a trinomial, if so factor it, if not explain why.

Answer 1

4x^2+12x+9 factorises to (2x+3)(2x+3) or (2x+3)^2, so the figure has side 2x+3 and is a square with perimeter 4(2x+3). So c=2 and d=3. The expression for the area is a quadratic trinomial, which is a two-dimensional property, but the area has three terms, involving one variable. The perimeter is a binomial having only one variable but two terms, variable and constant. When x=2' the perimeter is 4(4+3)=28 feet.