You plan to build a house that is [math]1\frac{1}{2}[/math] times as long as it is wide. You want the land around the house to be [b][i]20[/i][/b] feet wider than the width of the house, and twice as long as the length of the house, as shown below.
Write an expression for the area of the land surrounding the house. (Use decimal number)
Area of land surrounding the house = Area of land - Area of house[br][br]A = [math]\left(3x\right)\left(x+20\right)-\left(1.5x\right)\left(x\right)[/math][br][br]A = [math]3x^2+60x-1.5x^2[/math][br][br]A = [math]1.5x^2+60x[/math]
If [math]x=30[/math] feet, what is the area of the house?
A = [math]\left(x\right)\left(1.5x\right)[/math][br][br]A = [math]1.5x^2[/math][br][br]A = [math]1.5\left(30\right)^2[/math][br][br]A = 1350 sq ft
If [math]x=30[/math] feet, What is the area of the entire property?
A = [math]\left(3x\right)\left(x+20\right)[/math][br][br]A = [math]3x^2+60x[/math][br][br]A = [math]3\left(30\right)^2+60\left(30\right)[/math][br][br]A = 4500 sq ft