candy draws a square design with a side length of x inches for the window at the pet shop. she takes the…
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. what is the side length, in inches, of the pet shop sign? 4x + 5 4x - 5 8x + 5 8x - 5 16x² - 40x + 25
Answer
Explanation:
Step1: Recognize perfect - square trinomial
The formula for a perfect - square trinomial is $(a - b)^2=a^{2}-2ab + b^{2}$. For the trinomial $16x^{2}-40x + 25$, we have $a^{2}=16x^{2}$, so $a = 4x$, and $b^{2}=25$, so $b = 5$. Also, $-2ab=-2\times(4x)\times5=-40x$.
Step2: Factor the trinomial
Since $16x^{2}-40x + 25=(4x - 5)^{2}$.
Step3: Find the side - length of the square
The area of a square is $A = s^{2}$, where $s$ is the side - length. If $A=16x^{2}-40x + 25=(4x - 5)^{2}$, then $s = 4x-5$.
Answer:
B. $4x - 5$