Question

A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yd. as shown in figure below. The flagpole will take up a square plot with area x^2–8x+16 what is the length of the base of the flagpole.

Answer 1

Solution:-

According to question, a school is installing a flagpole in the central square plaza with side length 100 yd.

The flagpole will take up a square plot with area

Area = x²–8x+16 .

To find the length if the base of the flagpole.Let us make factors of the above expression by completing the square

Area = x^{​​​​​​2}​​​​​ -8x +16

Area = x^{​​​​​2} -2×4×x + (4)²

Area = (x -4)²

Area = (x-4)(x-4) ....(1)

Since area os square is a multiple of it's sides.

So, Area = side × side ....(2)

From equations (1) and (2) comparison , we get

Length of the base of flag post = x -4.

Hence, length of the flag post is (x-4).