Question

1. what is the length of side fh in triangle fgh

Explanation:

Step1: Apply the triangle inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let \(a = 6\), \(b=8\), and \(c\) be the length of \(FH\). Then \(|a - b|\lt c\lt a + b\).

Step2: Calculate the range

\(|6 - 8|=2\) and \(6 + 8 = 14\). So \(2\lt FH\lt14\). Without more information (like angles or type of triangle - right, isosceles etc.), we can only give the range based on the triangle inequality. If it's a right - triangle (assuming \(\angle G = 90^{\circ}\)):

Sub - step1: Use Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\), where \(a = 6\), \(b = 8\))

\(FH=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}\)

Answer:

If no additional information (e.g., right - triangle) is given, \(2\lt FH\lt14\). If it is a right - triangle with \(\angle G = 90^{\circ}\), \(FH = 10\) ft.