In a triangle the lengths of two sides are 5 and 9 and the length of the third side is represented by x. Which statement is always true?
বিকল্পসমূহ (নিজের উত্তর যাচাই করতে ক্লিক করুন):
সঠিক উত্তর
3 (4 < x < 14)
বিস্তারিত ব্যাখ্যা ও বিশ্লেষণ:
Solution:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. This is known as the Triangle Inequality Theorem.
Given that two sides of the triangle have lengths of 5 and 9, and the third side is represented by x, the theorem gives us the following inequalities:
1. x + 5 > 9, which simplifies to x > 4
2. x + 9 > 5, which is always true since x > -4
3. 5 + 9 > x, which simplifies to x < 14
Thus, the third side x must satisfy the condition:
4 < x < 14.
