Question

rt is a midsegment of \\( \triangle suv \\).
if \\( uv = p + 29 \\) and \\( rt = p \\), what is the value of \\( p \\)?

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of a midsegment of a triangle is half the length of the parallel side. So, \( UV = 2RT \).

Step2: Substitute the given expressions

Given \( UV=p + 29 \) and \( RT = p \), substitute into \( UV = 2RT \). We get \( p+29=2p \).

Step3: Solve for \( p \)

Subtract \( p \) from both sides of the equation \( p+29=2p \).
\( p+29 - p=2p - p \)
\( 29=p \)

Answer:

\( 29 \)