Question

triangle ijk is formed by connecting the midpoints of the side of triangle fgh. the lengths of the sides of triangle ijk are shown. what is the length of fh? figures not necessarily drawn to scale.

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of a mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
In triangle \(FGH\), since \(IJ\), \(IK\), and \(JK\) are mid - segments.
We know that if \(JK\) is a mid - segment parallel to \(FG\), \(IK\) is a mid - segment parallel to \(GH\), and \(IJ\) is a mid - segment parallel to \(FH\).
The length of the mid - segment \(IJ\) is related to the length of \(FH\) by the formula \(IJ=\frac{1}{2}FH\).

Step2: Solve for \(FH\)

Given that \(IJ = 7\).
From the formula \(IJ=\frac{1}{2}FH\), we can solve for \(FH\) by multiplying both sides of the equation by \(2\).
So, \(FH = 2\times IJ\).
Substitute \(IJ = 7\) into the equation: \(FH=2\times7\).

Answer:

\(14\)