Solve for x, then find the perimeter. You should select TWO answer choices. 18
3x
52
T
12
B
D
V
a
P= 140
x = 6
C
x = 18
d
P= 128

Answers:

x = 6 and P = 128

Explanation:

The tangents CT and CU are equal to each other. The rule is that tangent segments that meet at a common point are the same length.

Let's solve for x

CT = CU

3x = 18

x = 18/3

x = 6

Because CT = 18, this makes BC = BT+TC = 12+18 = 30

For similar reasoning as mentioned earlier, we can say tangents BT and BV are the same length. This means BV = 12.

Segment CD = 52 and CU = 18, which makes UD = CD-CU = 52-18 = 34

From there, we can say segment DV = 34 also. This leads to BD = BV+VD = 12+34 = 46

Triangle BCD has the three sides

The perimeter is

P = sum of the three sides

P = (side1)+(side2)+(side3)

P = BC + CD + BD

P = 30+52+46

P = 82+46

P = 128