Question

Which polynomial expression represents the area of the outermost square tile, shown below?
A. x2+6x − 6
B. x2 − 9x + 6
C. x2 + 6x − 9
D. x2 − 6x + 9

Answer 1

Answer:

Hence, option: D is correct.

The area of square tile is:

$x^2-6x+9$

Step-by-step explanation:

Clearly from the figure we could see that the side of the square tile is given to be:

x-3.

As we know that the area of a square with side length 's' is given to be:

Area=s^2

Hence, the area of this square tile is given by:

$Area=(x-3)^2\\\\Area=x^2+(3)^2-2\times x\times 3\\\\Area=x^2+9-6x$

Hence, the area of square tile with side length $x-3$ is given by:

$x^2-6x+9$

Answer 2

The area of the outermost square tile is $\boxed{{x^2} - 6x + 9}$.Option D is correct.

Further Explanation:

The formula of area of square can be expressed as follows,

$\boxed{Area = \left( s \right) \times \left( s\right)}$

The formula of perimeter of the rectangle can be expressed as follows,

$\boxed{{\text{Perimeter}} = 4 \times s}$

Here, s represents the side of square.

Given:

The options are as follows,

A. ${x^2} + 6x - 6$

B. ${x^2} - 9x + 6$

C. ${x^2} + 6x - 9$

D. ${x^2} - 6x + 9$

Explanation:

The side of the outermost square tile is $x-3.$

The area of the square can be obtained as follows,

$\begin{aligned}{\text{Area}} &= \left( {{\text{side}}} \right) \times \left( {{\text{side}}} \right) \\&=\left( {x - 3} \right)\left( {x - 3} \right)\\&= {\left( {x - 3} \right)^2} \\&= {x^2} - 2 \times \left( x \right) \times \left( 3 \right) + {\left( 9 \right)^2}\\&= {x^2} - 6x + 9\\\end{aligned}$

The area of the outermost square tile is $\boxed{{x^2} - 6x + 9}$. Option D is correct.

Option A is not correct.

Option B is not correct.

Option C is not correct.

Option D is correct.

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Mensuration

Keywords: rectangle, length, square, tile, polynomial expression, area, outermost tile, square tile, side of square, x-3, width, breadth, area of rectangle, dimension, measure of sides, dimensions of rectangle, expression, square.