Question

find the value of x.

Explanation:

Step1: Identify midsegment theorem

The segment $5x$ is the midsegment of the triangle, connecting midpoints of two sides. By the triangle midsegment theorem, the midsegment is half the length of the third side.

Step2: Set up equation

$$5x = \frac{90}{2}$$

Step3: Simplify and solve for x

$$5x = 45$$
$$x = \frac{45}{5}$$

Answer:

$x=9$