Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 - 40x + 25 square inches. A square labeled 16 x squared minus 40 x + 25 What is the side length, in inches, of the pet shop sign?

length of side of square = (4x - 5) inches

Step-by-step explanation:

We are given;

Area of square = 16x² - 40x + 25

Let's find the roots of this quadratic equation [-b ± √ (b² - 4ac) ]/2a

Thus;

x = [ - (-40) ± √ ((-40) ² - 4 (16 * 25) ] / (2*16)

x = [40 ± √ (1600 - 1600) ]/32

x = (40 ± 0) / 32

x = 40/32

x = 5/4

Thus, the factors of the polynomial are;

(4x - 5) ²

So,

Area = 16x² - 40x + 25 = (4x - 5) ²

Since, the right hand side is (4x - 5) ² and area of square is (length of side) ², thus we can say that length of side of square is (4x - 5) inches