Triangle Diagram

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

To find the value of x, we can use the fact that triangle URW is similar to triangle VWT.

The ratio of corresponding sides in similar triangles is equal. Therefore, we can set up the following equation:

12/3y = 15.9/11

Cross multiplying, we get:

12 * 11 = 3y * 15.9

132 = 47.7y

Dividing both sides by 47.7, we get:

y ≈ 2.77

Now, since triangle SUV is similar to triangle URW, we can use the same ratio to find the value of x:

2x/15.9 = 3y/12

Substituting the value of y we found:

2x/15.9 = 3 * 2.77 / 12

Simplifying:

2x/15.9 = 8.31 / 12

Cross multiplying:

2x * 12 = 8.31 * 15.9

24x = 132.42

Dividing both sides by 24:

x ≈ 5.51

Therefore, the value of x is approximately 5.51.

So, the correct answer is (5.5).