Answer:
The length of VU is 10 unit.
Explanation:
Consider the provided information.
The point P is equidistant from the vertices of ΔTUV, thus the segment PU equals to the segment PV, then these two segments are congruent:
PU=PV
Then ΔUVP is an isosceles triangle, because PU=PV.
Now, observe the provided figure, PR divides the ΔTUV in two triangle (ΔPUR and ΔPRV)
Where, ∠P=∠P, PR=PR and PV=PU. Thus ΔPUR congruent to ΔPRV and the legs UR and RV must be congruent:
UR = RV
3x - 1 = x + 3
Subtracting x from both side and add 1 to both sides of the above equation:
3x - 1 - x + 1 = x + 3 - x + 1
2x = 4
Divide both sides of the equation by 2:
x=2
VU = UR + RV
Where the length of UR is x + 3 and length of RV is 3x - 1.
Therefore, the length of UR is, 2+3=5
The length of RV is, 3(2)-1=5
Thus, the length of VU is 5+5=10.
Hence, the length of VU is 10 unit.