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mATH hELP

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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 6x^3 feet, and the rectangular plot of land has a length of 3x^5 feet and a width of 7x^2 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.

May 4, 2021

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For the square plot of land, the area is $$s^2$$, and the side lengths are $$6x^3$$, so $$6x^3 \cdot 6x^3 = 36x^6$$.

For the rectangular plot of land, the area is $$l \cdot w$$, and the length and width are $$3x^5$$ and $$7x^2$$, so $$3x^5 \cdot 7x^2 = 21x^7$$.

If $$x$$ is 3, then we put 3 for x.

$$36 \cdot 3^6 = 36 \cdot 729 = 26244$$sq ft

and

$$21 \cdot 3^7 = 21 \cdot 2187 = 45927$$sq ft.

So, the rectangular plot of land has a larger area.

May 4, 2021