Question

find k.
(there is a triangle with vertices h, i, j. point k is on hi, point l is on hj. hk and ki are marked with one red cross each, hl and lj are marked with two red parallel lines each. the segment kl is marked 18, and the segment ij is marked k.)
© algebra einstein, 2023

Explanation:

Step1: Use the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. Here, \(KL\) is the mid - segment of \(\triangle HIJ\).

Step2: Set up the proportion

Since \(KL = 18\), and by the mid - segment theorem \(KL=\frac{1}{2}IJ\). Let \(IJ = k\), then \(18=\frac{1}{2}k\).

Step3: Solve for \(k\)

Multiply both sides of the equation \(18=\frac{1}{2}k\) by \(2\). We get \(k = 18\times2\).

Answer:

\(k = 36\)