Final answer:
The length of an Olympic gymnastics floor with an area of 144 square meters is approximately 16 meters, assuming the floor's length is twice its width, which is consistent with standard dimension ratios.
Step-by-step explanation:
The question asks about the dimensions of a rectangular Olympic gymnastics floor with an area of 144 square meters. By definition, the area of a rectangle is the product of its length and width. As the width is not provided, but the area is known, we assume that an Olympic gymnastics floor is designed to meet specific international standards which usually dictate a length-to-width ratio of 2:1.
Let's denote the width as x meters. Therefore, the length would be 2x meters. The area A of the rectangle is given by the formula A = length × width. Substituting the known values, we have:
- 144 m2 = x × 2x
- 144 m2 = 2x2
- x2 = 72
- x = √72
- x = 8.49 meters (approximately)
Since we need an integer value answer, and the options given are 8, 10, 12, and 16 meters, we can approximate x to 8 meters. Thus, the length of the gymnastics floor would be 2 × 8 meters = 16 meters. The correct answer is option d. 16 meters.