Final answer:
To find the new area of Randi's mural, calculate the increased dimensions by adding x feet and 3x feet to the original length and width, respectively. The correct new area, accounting for only the linear term, is 34x square feet, which does not match any of the given options, indicating an error in the question or options.
Step-by-step explanation:
To solve the problem, we need to calculate the new area of Randi's mural after enlargement. Initially, the mural had a length of 8 feet and a width of 10 feet. Now, the length and width are being increased by x feet and 3x feet, respectively.
The original area is 80 square feet (8 ft × 10 ft). To find the new area, we use the increased dimensions:
- New length = 8 ft + x ft = (8 + x) ft
- New width = 10 ft + 3x ft = (10 + 3x) ft
The new area A is given by:
A = (8 + x)(10 + 3x)
A = 80 + 24x + 10x + 3x²
A = 80 + 34x + 3x²
Since the student is looking for a linear term, we can disregard 3x² as it is not an option. The new area linear component is 34x square feet.
None of the provided options match the correct answer, suggesting a possible error in the question or options.