Question

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 value of x?
(1 point)
Responses

6.5
6.5

6
6

11
11

5.5

Answer 1

[AI-generated answer — Bot GPT 3.5]

The value of x is 6.5.

In triangle URW, the sides are 12 and 15.9. Since U is the midpoint of RS, the side RW is half of ST, which means RW is 15.9/2 = 7.95.

In triangle VWT, the sides are 3y and 11. Since V is the midpoint of ST, the side WT is half of ST, which means WT is 15.9/2 = 7.95. Since W is the midpoint of TR, the side TW is half of TR, which means TW is 12/2 = 6.

Therefore, 3y = 6 and y = 2.

In triangle SUV, the sides are blank (ST) and 2x. Since SU is half of ST and is 7.95, we can solve for ST and then find 2x.

ST = 7.95 * 2 = 15.9

So, 2x = 15.9 and x = 15.9/2 = 7.95.

Therefore, x = 7.95 = 6.5.

Therefore, the value of x is 6.5.

Correct response: 6.5