To solve the previous problem, we can split the triangle into two right triangles, each having a base of 10 cm and a hypotenuse of 18 cm. The measure of the longer side is necessary to determine the height of the isosceles triangle. By applying the Pythagorean theorem, a² + b² = c², we have a² + (10cm)² = (18cm)², leading to a² = 324 cm² - 100 cm², thus a² = 224 cm². This results in a = √224 cm², which is approximately a = 14.97 cm. The area is then given by A = 1/2 * base * height, or A = 1/2 * 20 cm * 14.97 cm, yielding A = 149.70 cm². Using the formula A = r/2 * p, we derive 149.70 cm² = r/2 * (18cm + 18cm + 20cm), simplifying to 149.70 cm² = r/2 * 56 cm. This results in 149.70 cm² ÷ 56 cm = r/2. Consequently, r/2 equals 2.67 cm, and thus r is 5.34 cm. In conclusion, the final answer is that the radius is approximately 5.35 cm.
