ANSWER
The length base of the flag pole is (x - 4)
STEP-BY-STEP EXPLANATION:
From the question provided, you can see that the central plaza is a square and a flag pole will take up a square plot in the middle of the plaza.
The area of the flag pole is given below as
[tex]\text{Area o flagpole = x}^2-8x+16\text{ square yds}[/tex]The length of the plaza is 100 yds has given from the question provided
The next thing is to factorize the above quadratic function
[tex]\begin{gathered} \text{Area = x}^2\text{ - 8x + 16} \\ \text{Area = x}^2\text{ - 4x - 4x + 16} \\ \text{Area = x(x - 4) - 4(x - 4)} \\ \text{Area = (x - 4)(x - 4)} \\ \text{Area = (x - 4)}^2 \end{gathered}[/tex]Recall that, Area of a square is equivalent to the square of its given length
Hence,
[tex]\begin{gathered} \text{Area = length }\cdot\text{ length} \\ \text{Area = length}^2 \\ \text{ Recall that, area = (x - 4)}^2 \\ (x-4)^2=length^2 \\ \text{Take the square roots of both sides} \\ \sqrt[]{(x-4)^2}\text{ = }\sqrt[]{(length)^2} \\ \text{Length = x- 4} \end{gathered}[/tex]Hence, the length base of the flag pole is (x - 4)
