Question

if rs = w + 3 and qt = 2w, what is the value of w?

Explanation:

Step1: Apply the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides) is parallel to the third side and half its length. Here, \(QT\) is the mid - segment of \(\triangle URS\), so \(QT=\frac{1}{2}RS\).
Given \(RS = w + 3\) and \(QT = 2w\), we substitute into the equation: \(2w=\frac{1}{2}(w + 3)\).

Step2: Solve the equation

Multiply both sides of the equation \(2w=\frac{1}{2}(w + 3)\) by \(2\) to get rid of the fraction:
\(2\times2w=w + 3\), which simplifies to \(4w=w + 3\).
Subtract \(w\) from both sides: \(4w-w=w + 3-w\), so \(3w=3\).
Divide both sides by \(3\): \(w=\frac{3}{3}\).

Answer:

\(w = 3\)