In , U is the midpoint of , V is the midpoint of , and W is the midpoint of . Angle R is the bottom left, angle T is the bottom right, and angle S is the top. Inside is another equIn , U is the midpoint of , V is the midpoint of , and W is the midpoint of . 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?
To find the length of ?, we can use the side-length ratios of the equilateral triangles.
From triangle URW, we know that the side length of UR is 12 and the side length of RW is 15.9.
Since URW is an equilateral triangle, all its side lengths are equal, including UW.
Therefore, UW must also be 12.
From triangle VWT, we know that the side length of VT is 3y.
Since VWT is an equilateral triangle, the side length of VT is the same as the side length of UW.
So, 3y = 12.
Solving for y, we get: y = 4.
Therefore, the side length of VT is 3y = 3(4) = 12.
Now, let's focus on triangle SUV.
Since it is an equilateral triangle, the side length of SV is equal to the side length of UW.
So, SV = 12.
Since V is the midpoint of ST, and VT = 12, then VS = ST/2 = 12/2 = 6.
Therefore, the side length of SU is 12 - 6 = 6.
So, the length of SU is 6.
Therefore, the length of ? is 6.