Triangle Diagram
In triangle upper R upper S upper T, U is the midpoint of modifying above upper R upper S with bar, V is the midpoint of modifying above upper S upper T with bar, and W is the midpoint of Segment TR.
triangle
Angle R is the bottom left, angle T is the bottom right, and angle S is the top. Inside is another equilateral triangle facing down. Angle U is on the left, angle V is on the right, and angle W is the bottom. This forms four triangles within the larger triangle. Triangle URW has side lengths 12 and 15.9. Triangle VWT has side lengths 3y and 11. Triangle SUV has side lengths blank and 2x.
Question
Multiple Choice
Use the Triangle diagram to answer the question.
What is the length of modifying above upper U upper V with bar?
(1 point)
Responses
11
11
7.95
7.95
15.9
15.9
12
12
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To find the length of modifying above upper U upper V with bar, we can use the fact that W is the midpoint of Segment TR. Therefore, the length of Segment VW is equal to the length of Segment UW.
From the information given, we know that the length of Segment UW is 15.9. Therefore, the length of modifying above upper U upper V with bar is also 15.9.
The correct answer is 15.9.
To find the length of modifying above upper U upper V with a bar, we need to consider triangle UVW. We are given that triangle URW has side lengths 12 and 15.9, and that triangle VWT has side lengths 3y and 11.
Since U is the midpoint of segment RS, and V is the midpoint of segment ST, we can use the Midpoint Theorem to determine the length of modifying above upper U upper V with a bar. According to the theorem, the length of the segment joining the midpoints of two sides of a triangle is equal to half the length of the third side.
In this case, since W is the midpoint of segment TR, the length of upper UV with a bar would be half the length of segment TR, which is 15.9.
Therefore, the correct answer is 15.9.
To find the length of modifying above upper U upper V with bar, we need to look at triangle UVT. From the given information, we know that triangle URW has side lengths 12 and 15.9, and triangle VWT has side lengths 3y and 11.
Since triangle UVT is similar to triangle URW, we can set up the following proportion:
UT / UW = VT / RW
Substituting the known values, we get:
UT / 12 = VT / 15.9
To find the length of modifying above upper U upper V with bar, we need to find UT and VT.
Looking at triangle URW, we can see that UT is half the length of RW. Since RW is 15.9, UT is 15.9 / 2 = 7.95.
Looking at triangle VWT, we can see that VT is half the length of WT. Since WT is 11, VT is 11 / 2 = 5.5.
Now we can substitute the values back into the proportion:
7.95 / 12 = 5.5 / 15.9
Simplifying the equation:
0.6625 = 0.3459
This is not true, so the answer must be one of the given options.
From the response choices, the length of modifying above upper U upper V with bar is 7.95.