Ashwin paints 2 murals:
- A square mural in his classroom
- A mural in the hallway with length 7 feet longer and width 3 feet shorter
Also, x indicates the side length of the mural in the classroom. Since the classroom mural is square in shape, the length and breadth of the mural would be x.
Part A: Expression to represents the two binomials to be multiplied to find the area of the hallway mural
Area of the hallway mural = Length of the hallway mural × Breadth of the hallway mural
So Length of the hallway mural = Length of the classroom mural + 7
⇒ Length of the hallway mural = x + 7
Breadth of the hallway mural = Breadth of the classroom mural - 3
⇒ Breadth of the hallway mural = x - 3
Hence, x + 7 and x - 3 need to be multiplied to determine the area of the mural
Part B: Area of the hallway mural
Area of the hallway mural = Length of the hallway mural × Breadth of the hallway mural
⇒ Area of the hallway mural = (x + 7) × (x-3)
⇒ Area of the hallway mural = x² + 7x - 3x - 21
⇒ Area of the hallway mural = x² + 4x - 21
Part C: Area of the hallway mural if each side of the classroom mural is 8 foot long
Putting the value x = 8 in the answer of Part B
⇒ Area of the hallway mural = 8² + 4×8 - 21
⇒ Area of the hallway mural = 64 + 4×8 - 21
⇒ Area of the hallway mural = 64 + 32 - 21
⇒ Area of the hallway mural = 75 square feet
