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, we use the formula: area = side length^2
For the square plot of land with a side length of 6x^3 feet, the area would be:
Area = (6x^3)^2
Area = 36x^6 square feet
To find the area of a rectangle, we use the formula: area = length x width
For the rectangular plot of land with a length of 3x^5 feet and a width of 7x^2 feet, the area would be:
Area = (3x^5)(7x^2)
Area = 21x^7 square feet
Now, we can determine which plot of land has a larger area when x = 3:
For the square plot: Area = 36(3)^6 = 729 * 36 = 26,244 square feet
For the rectangular plot: Area = 21(3)^7 = 2187 * 21 = 45,927 square feet
Therefore, when x = 3, the rectangular plot of land has a larger area.