Question

Jacob helps paint a square mural in his classroom. Then he helps paint a mural in the hallway whose length is 6 feet longer and whose width is 2 feet 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 8 feet long.
20 Minutes, 59 Seconds
0(x- 6)(x+ 2)
20 square feet
0(x+6)(x+2)
140 square feet
0(x- (x-6)(x-2)
12 square feet
0(x+ (x+6)(x-2)
84 square feet

Answer 1

To find the area of the hallway mural in relation to the side length \( x \) of the mural in Jacob's classroom, we start by establishing the dimensions of the hallway mural.

1. **Side length of the classroom mural:** \( x \)
2. **Length of the hallway mural:** \( x + 6 \) (which is 6 feet longer)
3. **Width of the hallway mural:** \( x - 2 \) (which is 2 feet shorter)

The area \( A \) of the hallway mural can be expressed as:
\[
A = \text{Length} \times \text{Width} = (x + 6)(x - 2)
\]

Now we can expand this expression:
\[
A = (x + 6)(x - 2) = x^2 - 2x + 6x - 12 = x^2 + 4x - 12
\]

Next, if each side of the classroom mural is 8 feet long, we substitute \( x = 8 \) into the area expression for the hallway mural:
\[
A = (8 + 6)(8 - 2) = (14)(6) = 84 \text{ square feet}
\]

So, the expression that represents the area of the hallway mural is \( (x + 6)(x - 2) \), and when \( x = 8 \), the area of the hallway mural is \( 84 \) square feet.

The correct conclusion is:
**The area of the hallway mural is 84 square feet.**