Question

guided practice
midsegments of triangles
type your answer and then click or tap done.
what is the value of x?

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of the midsegment of a triangle (a segment connecting the midpoints of two sides) is half the length of the third side. Here, \(ED\) is the midsegment and \(CB\) is the third side. So, \(ED=\frac{1}{2}CB\).

Step2: Substitute the given values

We know \(ED = 14\) and \(CB=x - 2\). Substituting into the equation \(14=\frac{1}{2}(x - 2)\).
Multiply both sides by 2: \(14\times2=x - 2\), which gives \(28=x - 2\).
Add 2 to both sides: \(x=28 + 2\).

Answer:

\(x = 30\)