Question

ij is a midsegment of \\( \triangle fgh \\). ij = 7, fh = 9, and gh = 12. find the perimeter of \\( \triangle ijh \\).

the perimeter of \\( \triangle ijh \\) is \\( \square \\).

Explanation:

Step1: Use the mid - segment theorem

Since \(IJ\) is a mid - segment of \(\triangle FGH\), by the mid - segment theorem, \(IJ=\frac{1}{2}FG\), so \(FG = 2IJ\). Given \(IJ = 7\), then \(FG=14\). Also, \(HI=\frac{1}{2}FH\) and \(HJ=\frac{1}{2}HG\). Given \(FH = 9\), so \(HI=\frac{9}{2}=4.5\). Given \(GH = 12\), so \(HJ=\frac{12}{2}=6\).

Step2: Calculate the perimeter of \(\triangle IJH\)

The perimeter of \(\triangle IJH\) is \(P=IJ + HI+HJ\). Substitute \(IJ = 7\), \(HI = 4.5\), and \(HJ = 6\) into the formula: \(P=7 + 4.5+6\).

Answer:

\(17.5\)