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 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 the side of triangle SUV, we can use the fact that triangle UVW is an equilateral triangle.
Since U is the midpoint of SR and V is the midpoint of RT, we can conclude that UV is also the base of triangle SRV.
Therefore, the length of UV is equal to the length of SR and RT, which are both 15.9.
Therefore, the length of UV is 15.9.
Since triangle UVW is equilateral, this means that the lengths of all sides are equal, including UW.
Since the length of UW is 12, this means that the length of UV is also 12.
Therefore, the length of UV is 12.
To find the length of side SU, we can use the fact that SU is the midpoint of RW.
Therefore, the length of SU is half the length of RW.
Since RW is 12, this means that SU is 6.
To find the length of side SV, we can use the fact that SV is the midpoint of WT.
Therefore, the length of SV is half the length of WT.
Since WT is 11, this means that SV is 5.5.
Therefore, the lengths of the sides of triangle SUV are 6 and 5.5.
So, the correct answer is 6 and 5.5.