Question

find the value of the variable.
(there is a triangle diagram with segments labeled 16, 28, 36, and a variable q, along with a blank to fill in the value of q)

Explanation:

Step1: Apply the triangle - proportionality theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Here, we can set up the proportion \(\frac{16}{d}=\frac{28}{36}\).

Step2: Cross - multiply to solve for \(d\)

Cross - multiplying gives us \(28d = 16\times36\). First, calculate \(16\times36=576\). So the equation becomes \(28d = 576\).

Step3: Solve for \(d\)

Then, \(d=\frac{576}{28}\). Simplify \(\frac{576}{28}=\frac{144}{7}\approx20.57\).

Answer:

\(d = \frac{144}{7}\)