Answer:
x = 10.5
Step-by-step explanation:
Firstly, in geometry, you may have to prove that the two triangles pictured are similar.
Since the two horizontal lines are marked, they are assumed to be parallel.
Therefore, if the lines are parallel, the two bottom angles of each triangle can be treated as the same due to the [Corresponding Angles Theorem], respectively
As such, the two triangles can be seen as SIMILAR as proven by Angle-Angle Similarity.
Now that we've proven both triangles to be similar, we can then set up ratios for the sides:
[tex]\frac{8}{6}[/tex] = [tex]\frac{8+14}{y}[/tex]
Note: we are using y as a measure of the entire right side of the triangle, so
y = 6 + x
Continuing on, if you cross-multiply the fractions to solve for y:
8y = 6 * 22
Simplify.
8y = 132
Simplify again.
y = 16.5
We are not done yet! We are solving for x, so remember y = 6 + x
16.5 = 6 + x
Solve for x.
x = 10.5
