Question

g is the midpoint of \\(\overline{hk}\\) and i is the midpoint of \\(\overline{hj}\\). if \\(jk = t + 5\\) and \\(gi = 3t\\), what is the value of \\(t\\)?

Explanation:

Step1: Apply the mid - segment theorem

Since \(G\) is the midpoint of \(\overline{WK}\) and \(I\) is the midpoint of \(\overline{WJ}\), by the mid - segment theorem in a triangle (\(GI\) is parallel to \(KJ\) and \(GI=\frac{1}{2}KJ\)).

Step2: Set up the equation

Given \(KJ = t + 5\) and \(GI=34\). Substitute into the formula \(GI=\frac{1}{2}KJ\), we get \(34=\frac{1}{2}(t + 5)\).

Step3: Solve the equation for \(t\)

Multiply both sides of the equation \(34=\frac{1}{2}(t + 5)\) by \(2\): \(2\times34=t + 5\), so \(68=t + 5\).
Subtract \(5\) from both sides: \(t=68 - 5\).

Answer:

\(t = 63\)