Answer:
TZ = 24
Step-by-step explanation:
Similar Triangles
If two triangles are similar, then:
* All the corresponding side lengths are proportional by the same scale factor
* All the internal angles are congruent.
The image provided in the question has two similar triangles TYZ and TWX. We have completed the shape with a variable p =TZ, whose value will be determined by applying the first similarity condition above.
The ratio between the heights is 20:16, and the proportion between the bases is (6+p):p, thus:
[tex]\displaystyle \frac{6+p}{p}=\frac{20}{16}=\frac{5}{4}[/tex]
Cross-multiplying denominators:
4(6 + p) = 5p
24 + 4p = 5p
Solving for p:
p = 24
Then, TZ = 24
