Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x3 feet, and the rectangular plot of land has a length of 3x5 feet and a width of 7x2 feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3
.(4 points)
To find the area of a square, you simply square the length of one of its sides. In this case, the side length of the square plot of land is 6x3 feet. So the area of the square plot is:
Area of square = (6x3)^2 = 36x^6 square feet
To find the area of a rectangle, you multiply its length and width. In this case, the length of the rectangular plot of land is 3x5 feet and the width is 7x2 feet. So the area of the rectangular plot is:
Area of rectangle = (3x5) * (7x2) = 21x^5 * 14x^2 = 294x^7 square feet
Now, when x is 3, we can substitute x=3 into the expressions to find the actual areas of the plots:
Area of square = 36*(3)^6 = 36*729 = 26244 square feet
Area of rectangle = 294*(3)^7 = 294*2187 = 641478 square feet
Therefore, when x is 3, the rectangular plot of land has a larger area compared to the square plot.