Final answer:
Using the Pythagorean theorem on the right triangles formed by the altitude CD, we find that AC is approximately 2.29 cm, but this answer doesn't match any of the provided options.
Step-by-step explanation:
In triangle ABC, with CD as an altitude and AD equal to BC, if AB is given as 3 cm and CD is √3 cm, we can use the Pythagorean theorem to find AC. Since AD = BC and CD is an altitude, triangles ACD and BCD are right triangles. Since AB = AD + DB and AD = DB (because AD = BC and D is the midpoint), we can set up the equation AD2+ CD2 = AC2. With AD being half of AB (1.5 cm), we can calculate AC2 = 1.52 + (√3)2.
AC2 = 2.25 + 3 = 5.25, so AC = √5.25 = approximately 2.29 cm. However, none of the options provided matches this value, which indicates there may be a mistake in the setup of the problem or in the provided options. In such cases, it's important to review the information given and ensure there are no misunderstandings in the problem's setup.