Question

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if gh = w and ik = w - 22, what is the value of w?
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Explanation:

Step1: Identify Midline Theorem

In triangle \(GHJ\), \(I\) is midpoint of \(HJ\) and \(K\) is midpoint of \(GJ\) (from tick marks). So \(IK\) is midline, meaning \(IK=\frac{1}{2}GH\).

Step2: Substitute Given Expressions

Given \(GH = w\) and \(IK = w - 22\), substitute into midline formula: \(w - 22=\frac{1}{2}w\).

Step3: Solve for \(w\)

Subtract \(\frac{1}{2}w\) from both sides: \(w-\frac{1}{2}w - 22 = 0\) → \(\frac{1}{2}w=22\). Multiply both sides by 2: \(w = 44\).

Answer:

\(44\)