Question

find the value of x.
x =

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle is half the sum of the lengths of the parallel sides. Here, we can set up the proportion \(\frac{x}{27 + 22}=\frac{2}{3}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{x}{49}=\frac{2}{3}\) gives \(3x = 49\times2\). Then \(3x=98\), and \(x=\frac{98}{3}\approx32.67\). Wait, no. Let's re - check.

Wait, another approach: If we consider the ratio of the segments. Let's assume the triangle is divided proportionally. The ratio of the smaller part to the whole for the side with length \(22\) and \(27\) is \(\frac{2}{3}\) (since the mid - segment - like line divides the sides proportionally). Let the length of the side parallel to \(x\) be \(y\). Using the property of similar triangles (or the basic proportionality theorem). If we assume the lines divide the sides proportionally. Let's use the formula \(x = 2\times22 - 27\).

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Answer:

\(x = 17\)