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
.
To find the area of a square, you simply square the length of one side. So for the square plot of land with a side length of 6x^3 feet, the area would be (6x^3)^2 = 36x^6 square feet.
To find the area of a rectangle, you multiply the length by the width. So for the rectangular plot of land with a length of 3x^5 feet and a width of 7x^2 feet, the area would be 3x^5 * 7x^2 = 21x^7 square feet.
Now, let's substitute x=3 into the expressions for area:
For the square plot, the area would be 36(3)^6 = 36(729) = 26244 square feet.
For the rectangular plot, the area would be 21(3)^7 = 21(2187) = 45867 square feet.
Therefore, based on the calculations, the rectangular plot of land has a larger area when x=3.