Final answer:
Using the formula for volume in terms of mass and density, and the fact that volume is also the product of a rectangle's dimensions, we calculate the length of the rectangular solid to be 6.23 cm, which is not listed in the provided options.
Step-by-step explanation:
To find the length of a rectangular solid, we use the relationship between its mass, volume, and density. Given that density (ρ) is mass (m) divided by volume (V), V can be expressed as m/ρ. The volume of a rectangular solid is also the product of its length (l), width (w), and thickness (t). Therefore, l can be found by rearranging the formula to l = V / (w * t). In this case, the mass of the solid is 95.5 g, and the density is 3.5 g/cm³. The volume is thus 95.5 g / 3.5 g/cm³ = 27.2857 cm³. With a width of 2.50 cm and a thickness of 1.75 cm, the length is 27.2857 cm³ / (2.50 cm * 1.75 cm) = 27.2857 cm³ / 4.375 cm² = 6.23 cm.
Hence, none of the provided options (A: 10 cm, B: 15 cm, C: 20 cm, D: 25 cm) is correct. The length of the solid is approximately 6.23 cm.