Given triangle ABC. AB is the base, CD is the height. AC = 3cm, CD = √8 cm. Find AB, BC, AD, BD.

An error was made in the problem statement. It is not indicated that triangle ABC is isosceles.

1. Calculate the length of the segment AD. For the calculation, we use the Pythagorean theorem:

AD = √AC²- CD² = √3² – (√8) ² = √9 – 8 = √1 = 1 centimeter.

2. In an isosceles triangle, the height CD also serves as a median and divides

side AB into two equal segments. Therefore, AD = BD = 1 centimeter.

3. According to the condition of the problem, AB is the base. So AC and BC are the sides. In isosceles

they have the same length in the triangle, that is, AC = BC = 3 centimeters.

4. AB = AD + BD = 1 + 1 = 2 centimeters.

Answer: AB = 2 centimeters, BC = 3 centimeters. AD = BD = 1 centimeter.