Question

ij is a midsegment of \\( \triangle fgh \\). \\( ij = 11 \\), \\( fh = 18 \\), and \\( gh = 21 \\). 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, \(IJ=\frac{1}{2}FG\), \(HI = \frac{1}{2}FH\), and \(HJ=\frac{1}{2}GH\). Given \(IJ = 11\), \(FH = 18\), and \(GH = 21\).
We can find \(HI=\frac{1}{2}\times FH=\frac{1}{2}\times18 = 9\) and \(HJ=\frac{1}{2}\times GH=\frac{1}{2}\times21 = 10.5\)

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

The perimeter \(P\) of \(\triangle IJH\) is \(P=IJ + HI+HJ\).
Substitute \(IJ = 11\), \(HI = 9\), and \(HJ = 10.5\) into the formula: \(P=11 + 9+10.5\)

Step3: Simplify the expression

\(P=(11 + 9)+10.5=20 + 10.5=30.5\)

Answer:

\(30.5\)