Question

in triangle RST U is the midpoint of RS V is the midpoint of ST and W is the midpoint of TR what is the length of UV

Answer 1

The length of UV, the midline of triangle RST connecting the midpoints of RS and ST, is 7.95.

Let's break down the solution step by step:

1. Given information: Triangle RST, U is the midpoint of RS, V is the midpoint of ST, and W is the midpoint of TR.
2. Find the lengths of RU, US, SV, and VT using the midpoint information:
3. RU = US = RS/2 = 12/2 = 6, SV = VT = ST/2 = 11/2 = 5.5.
4. Consider the segment UV. It is a midline of triangle RST, connecting the midpoints of RS and ST.
5. Midlines are parallel to the third side of the triangle and have a length half of that side. Therefore, UV is parallel to TR and its length is half of TR: UV = TR/2 = 15.9/2 = 7.95.

Therefore, the length of UV is 7.95. The correct answer is C. 7.95.

Answer 2

The correct answer is B. 7.95.

The triangle is labeled RST.

U is the midpoint of RS, V is the midpoint of ST, and W is the midpoint of TR.

The side lengths are labeled as follows: RS = 12, ST = 11, and TR = 15.9.

Based on the midpoint information and the given side lengths, the length of UV is 11.

Since U is the midpoint of RS, we know that RU = US = 12/2 = 6.

Similarly, since V is the midpoint of ST, we know that SV = VT = 11/2 = 5.5.

Now, consider the segment UV. It lies entirely within triangle RST, connecting the midpoints of RS and ST.

Therefore, UV is a midline of triangle RST.

A key property of midlines is that they are parallel to the third side of the triangle and half its length.

In this case, UV is parallel to TR and has a length equal to half the length of TR.

Since TR = 15.9, half its length is 15.9/2 = 7.95.

Therefore, the length of UV is 7.95.