Question

Три точки В, С и D лежат на одной прямой. Известно, что ВD =17см, DС =25см. Какой может быть длинна отрезка ВС? Решить двумя способами.

Answer 1

1)BC = 25-17=8
2)BC = 25+17=42

Answer 2

#### Problem Analysis We are given three points, B, C, and D, that lie on a straight line. The lengths of BD and DC are given as 17 cm and 25 cm, respectively. We need to determine the possible length of segment BC. Let's solve this problem using two different methods. #### Method 1: Using the Segment Addition Postulate The Segment Addition Postulate states that if three points A, B, and C are collinear, then the distance between A and C is equal to the sum of the distances between A and B, and B and C. In this case, we can use the Segment Addition Postulate to find the length of segment BC. Let's denote the length of segment BC as x. According to the Segment Addition Postulate, we have: BD + DC = BC Substituting the given values, we get: 17 cm + 25 cm = x Simplifying the equation, we find: 42 cm = x Therefore, the length of segment BC is **42 cm**. #### Method 2: Using the Pythagorean Theorem Another way to solve this problem is by using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we can consider triangle BCD as a right triangle, with BD as the hypotenuse. Let's denote the length of segment BC as x. Using the Pythagorean Theorem, we have: BD^2 = BC^2 + DC^2 Substituting the given values, we get: 17 cm^2 = x^2 + 25 cm^2 Simplifying the equation, we find: 289 cm^2 = x^2 + 625 cm^2 Rearranging the equation, we get: x^2 = 289 cm^2 - 625 cm^2 x^2 = -336 cm^2 Since the square of a length cannot be negative, there is no real solution for x^2 = -336 cm^2. Therefore, there is no possible length for segment BC in this case. To summarize: - Using the Segment Addition Postulate, the length of segment BC is **42 cm**. - Using the Pythagorean Theorem, there is no possible length for segment BC. Please let me know if you need any further clarification or assistance!