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 ofmodifying above upper R upper S with bar?
(1 point)
Responses
12
12
6
6
22
22
24
24
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To find the length of modifying above upper R upper S with bar, we can use the fact that U is the midpoint of modifying above upper R upper S with bar.
Since triangle URW is a right triangle, we can use the Pythagorean theorem:
(12)^2 + (15.9)^2 = (modifying above upper R upper S with bar)^2
Simplifying the equation:
144 + 252.81 = (modifying above upper R upper S with bar)^2
396.81 = (modifying above upper R upper S with bar)^2
Taking the square root of both sides:
(modifying above upper R upper S with bar) = √396.81
(modifying above upper R upper S with bar) = 19.92
Therefore, the length of modifying above upper R upper S with bar is 19.92.
To find the length of the line segment modifying above upper R upper S with bar, we need to focus on the triangle URW.
We are given that triangle URW has side lengths 12 and 15.9. Since U is the midpoint of modifying above upper R upper S with bar, we know that the length of RS is twice the length of UR. Therefore, RS = 2 * UR.
From the given information, we have UR = 12. We can substitute this value into the equation RS = 2 * UR to find RS.
RS = 2 * 12
RS = 24
Therefore, the length of RS is 24. So, the correct answer is 24.