Points E, D, and H are the midpoints of triangle TUV. UV=80, TV=100, and HD=80. Find TU.

triangle HVD is similar to triangle TVU. ratio of corresponding sides are equal
[tex] \frac{vd}{vu} = \frac{hd}{tu} [/tex]
Since D is the midpoint of VU, VD=40
[tex] \frac{40}{80} = \frac{80}{tu} [/tex]
40(TU)=80(80)
[tex]tu = \frac{80 \times 80}{40} \\ tu = 160[/tex]

Answer Link

psm22415 psm22415 · Answer 2 · 2021-12-15T07:20:29+01:00

The required length of TU is 160.

Given that,

Points E, D, and H are the midpoints of triangle TUV.

UV = 80, TV = 100, and HD = 80.

We have to determine,

The length of TU.

According to the question,

Points E, D, and H are the midpoints of triangle TUV.

In the triangle, HVD is similar to triangle TVU. the ratio of corresponding sides is equal.

Then,

[tex]\dfrac{VD}{VU} = \dfrac{HD}{TU}[/tex]

Here, The length of VU = 80 and VD is half of VU = 40

Substitute the values in the equation,

[tex]\dfrac{40}{80} = \dfrac{80}{TU}\\\\TU = \dfrac{80 \times 80}{40}\\\\TU = 160[/tex]

Hence, The required length of TU is 160.

To know more about Triangles click the link given below.

https://brainly.com/question/1863222