Question

The area of a square in square feet is

Answer 1

Answer:

Part 1) The expression for the perimeter is $P=4(25z-3)$ or  $P=100z-12$

Part 2) The perimeter when  z = 15 ft. is $P=1,488\ ft$

Step-by-step explanation:

Part 1)

we have

$625z^{2}-150z+9$

Find the roots of the quadratic equation

Equate the equation to zero

$625z^{2}-150z+9=0$

Complete the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$625z^{2}-150z=-9$

Factor the leading coefficient  

$625(z^{2}-(150/625)z)=-9$

$625(z^{2}-(6/25)z)=-9$

Complete the square. Remember to balance the equation by adding the same constants to each side

$625(z^{2}-(6/25)z+(36/2,500))=-9+(36/4)$

$625(z^{2}-(6/25)z+(36/2,500))=0$

Rewrite as perfect squares

$625(z-6/50)^{2}=0$

$z=6/50=0.12$ -----> root with multiplicity 2

so

The area is equal to  

$A=625(z-0.12)(z-0.12)=[25(z-0.12)][25(z-0.12)]=(25z-3)^{2}$

The length side of the square is $b=(25z-3)$

therefore

The perimeter is equal to

$P=4b$

$P=4(25z-3)$

$P=100z-12$

Part 2) Find the perimeter when  z = 15 ft.

we have

$P=100z-12$

substitute the value of z

$P=100(15)-12=1,488\ ft$