Question

1. error analysis a student said that a triangle with side lengths of 3 ft and 4 ft could have a third side with a length of 7 ft. explain why the student is incorrect. what is a correct statement about the third side of the triangle?

Explanation:

Step1: Apply triangle side - length relationship

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let \(a = 3\), \(b=4\), and \(c = 7\). Check \(a + b>c\).
\(3+4=7\), but \(7
ot>7\).

Step2: Find the range of the third side

Let the third - side length be \(x\). According to the triangle inequality theorem: \(|a - b|Since \(a = 3\) and \(b = 4\), then \(|3 - 4|

Answer:

The student is incorrect because \(3 + 4=7\), and the sum of two sides of a triangle must be greater than the third side. The correct statement is that the length \(x\) of the third side satisfies \(1\mathrm{ft}