Question

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

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. In triangle \(ABC\), \(DE\) is the mid - segment (\(D\) is the midpoint of \(AB\) and \(E\) is the midpoint of \(BC\)). So, \(DE=\frac{1}{2}AC\).

Step2: Substitute the given values

We know that \(AC = 40\) and \(DE=5x\). Substituting into the formula \(5x=\frac{1}{2}\times40\).

Step3: Solve for \(x\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times40 = 20\). Then we have the equation \(5x=20\). Divide both sides by \(5\): \(x=\frac{20}{5}\).

Answer:

\(x = 4\)