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. A. $$ (x+6)(x-2) ; 84 $$ square feet B. $$ (x-6)(x-2) ; 12 $$ square feet C. $$ (x+6)(x+2) ; 140 $$ square feet D. $$ (x-6)(x+2) ; 20 $$ square feet

Question

UpStudy AI · Accepted Answer

To solve the problem, let's break it down step by step:

1. **Classroom Mural:**
   - It's a square mural, so both the length and width are $$ x $$ feet.
   - Area of the classroom mural: $$ x \times x = x^2 $$ square feet.

2. **Hallway Mural:**
   - **Length:** 6 feet longer than the classroom mural, so $$ x + 6 $$ feet.
   - **Width:** 2 feet shorter than the classroom mural, so $$ x - 2 $$ feet.
   - **Area Expression:** To find the area of the hallway mural, multiply the length and width:
     $$
     (x + 6)(x - 2)
     $$

3. **Calculating the Area:**
   - Given that each side of the classroom mural is 8 feet long ($$ x = 8 $$):
     $$
     (8 + 6)(8 - 2) = 14 \times 6 = 84 \text{ square feet}
     $$

**Therefore, the correct answer is:**

**A. $$ (x+6)(x-2) ; 84 $$ square feet**
The area of the hallway mural is $$ (x+6)(x-2) $$ square feet, and when $$ x = 8 $$, the area is 84 square feet.

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions