Answer:
x = 4
Step-by-step explanation:
You want the value of x in the figure shown.
Similar triangles
The two triangles in the figure are similar. (They share the acute angle at lower left, and they each have a right angle, so are similar by the AA postulate.)
This means corresponding sides are proportional. The ratio of vertical side to horizontal side is ...
[tex]\dfrac{x}{7.5}=\dfrac{8}{7.5+7.5}\\\\x=(7.5)\dfrac{8}{15}=\dfrac{8}{2}\\\\\boxed{x=4}[/tex]
Alternate solution
Another way to solve this is to recognize that the segment marked x is parallel to the one marked 8, and meets the bottom segment at its midpoint. That makes "x" be the midline of the triangle. The midline is always half the length of the base, so x = 8/2 = 4.
