Question

question 31 of 50
\overline{bd} is a midsegment of triangle ace and bd is parallel to ae.
the value of x is:
triangle ace with midsegment bd, bd=24, ae=x; multiple choice options: 48, 12, 24

Explanation:

Step1: Recall Midsegment Theorem

The Midsegment Theorem (also known as the Midline Theorem) states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side. In triangle \(ACE\), \(BD\) is a midsegment, so \(BD\parallel AE\) and \(BD=\frac{1}{2}AE\).

Step2: Apply the Theorem to Find \(x\)

We know \(BD = 24\) from the diagram. Using the Midsegment Theorem: \(BD=\frac{1}{2}AE\), so \(AE = 2\times BD\). Substituting \(BD = 24\), we get \(AE=2\times24 = 48\). Since \(AE=x\), then \(x = 48\).

Answer:

48 (corresponding to the option "48")