Question

Jacob helps paint a square mural in his classroom. Then he helps paint a mural in the hallway whose length is $6\mathrm{feet}$ longer and whose width is $2feet$ shorter. Let $x$ represent the side length of the mural in Jacob's classroom. Write an expression that represents the two binomials you would multiply to find the area of the hallway mural. Use that expression to find the area of the hallway mural if each side of the classroom mural is $8feet$long.

Answer 1

Finding the area of halfway mural:

Let side length of the square mural $=x$

According to statement:

Length of the halfway mural $=x+6$ $...\left[1\right]$

Width of the halfway mural $=x-2$ $...\left[2\right]$

$\Rightarrow$ Halfway mural is rectangle.

We know that area of rectangle $A=l\times b$, where $l$ is the length and $b$ is the width of rectangle.

$\Rightarrow$ Area of halfway mural $A=\left(x+6\right)\left(x-2\right)$ $...\left[3\right]$ [Put $l=x+6$ and $b=x-2$]

Put $x=8$ in $\left[3\right]$, we get

$\therefore A=\left(8+6\right)\left(8-2\right)$

$\Rightarrow$$A=14\times 6$

$\Rightarrow$$A=84$

Hence, expression is $\left(x+6\right)\left(x-2\right)$ and area of halfway mural is $84fee{t}^2$.