Question

if st = w and pr = w - 37, what is the value of w? s t r p q w =

Explanation:

Step1: Identify Midsegment Theorem

In triangle \(QST\), \(R\) is the midpoint of \(QS\) and \(P\) is the midpoint of \(QT\), so \(PR\) is the midsegment. The midsegment is half the length of the parallel side \(ST\).

Step2: Set up the equation

From the theorem: \(PR = \frac{1}{2}ST\). Substitute \(ST = w\) and \(PR = w - 37\):
\(w - 37 = \frac{1}{2}w\)

Step3: Solve for \(w\)

Subtract \(\frac{1}{2}w\) from both sides:
\(w - \frac{1}{2}w - 37 = 0\)
\(\frac{1}{2}w = 37\)
Multiply both sides by 2:
\(w = 37 \times 2\)

Answer:

74