Points E, D, and H are the midpoints of the sides of TUV, UV = 74, TV = 96, and HD = 74 Find TU -

Answer 1

Let's first draw a diagram to visualize the problem:

```
T
/ \
/ \
U-----V
```

We know that E, D, and H are the midpoints of sides TU, TV, and UV respectively. Therefore, segments TE, UD, and VH are all equal in length.

We are given that UV = 74, TV = 96, and HD = 74.

Since D is the midpoint of TV, we can find the length of TD by subtracting the length of HD from TV:

TD = TV - HD = 96 - 74 = 22.

Since E is the midpoint of TU, we can find the length of TE by subtracting the length of ED from TU:

TE = TU - ED.

Since D is the midpoint of UV, ED is half the length of UV:

ED = UV/2 = 74/2 = 37.

Substituting this value into the previous equation, we have:

TE = TU - 37.

We can see that TE is equal to half the length of TD because E and D are both midpoints:

TE = TD/2 = 22/2 = 11.

Now we can find the length of TU:

TU = TE + EU = 11 + 11 = 22.

Therefore, TU - TD = 22 - 22 = 0.