Question

Consider the figure below:

20
16
6
Determine the length of TZ.
Do not include spaces, units, or commas in your response.
Enter answer here. Do not include spaces or units.

Answer 1

TZ = 24

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:

`\displaystyle (6+p)/(p)=(20)/(16)=(5)/(4)`

Cross-multiplying denominators:

4(6 + p) = 5p

24 + 4p = 5p

Solving for p:

p = 24

Then, TZ = 24