Question

question 5 of 50
\\(\overline{be}\\) is the midsegment of triangle acd. the value of x is
image of triangle acd with midsegment be, segment be labeled x + 5, segment cd labeled 54, and multiple choice options: 25, 49, 22, 27, 32

Explanation:

Step1: Recall Midsegment Theorem

The midsegment of a triangle is parallel to the third side and half its length. So \( BE=\frac{1}{2}CD \).

Step2: Set Up Equation

Given \( BE = x + 5 \) and \( CD = 54 \), substitute into the formula: \( x + 5=\frac{1}{2}\times54 \).

Step3: Solve for x

First, calculate \( \frac{1}{2}\times54 = 27 \). Then, \( x + 5 = 27 \). Subtract 5 from both sides: \( x=27 - 5=22 \).

Answer:

22