Final answer:
The area of the actual patio is calculated by multiplying the real dimensions, 15 ft by 7.5 ft, resulting in 112.5 sq. ft. which does not match the options given in the question.
Step-by-step explanation:
The correct answer is option B) 27 sq. ft.
To find the area of the actual patio using the scale model, you must first understand that the scale model is not providing direct measurements of the actual patio but is instead a representation. The given scale model of the patio is 6 feet long and 3 feet wide. To calculate the area of the scale model, multiply the length by the width:
- Scale model area = length × width = 6 ft × 3 ft = 18 sq. ft.
However, we are given that the actual length of the patio is 15 feet, which is 2.5 times longer than the scale model length (because 15 ft / 6 ft = 2.5). Thus, to keep the proportions the same, the width of the actual patio must also be 2.5 times the scale model width. Therefore, the actual patio measures 15 ft by 7.5 ft (since 3 ft × 2.5 = 7.5 ft). Calculating the area of the actual patio gives us:
- Actual patio area = length × width = 15 ft × 7.5 ft = 112.5 sq. ft.
This area does not match any of the options provided, suggesting there may be a mistake in the question or the options given are incorrect.