Answer: 128 units
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Step-by-step explanation:
Segments JK, KL, and JL are tangent to the circle.
We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:
Let's use the first equation to solve for x.
MJ = NJ
5x-8 = 8x-35
5x-8x = -35+8
-3x = -27
x = -27/(-3)
x = 9
Use the same idea to find y.
KN = KO
7y-9 = 2y+11
7y-2y = 11+9
5y = 20
y = 20/5
y = 4
Now compute the length of segment KO.
KO = 2y+11 = 2*4+11 = 19 units
Subtract this from LK to find LO
LO = LK - KO
LO = 32 - 19
LO = 13
This makes segment LM to be also 13 units long.
Now use the value of x to find sides MJ and NJ
MJ = 5x-8 = 5*9-13 = 32
NJ = 32 as well
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We have these pieces:
- MJ = NJ = 32
- KN = KO = 19
- LM = LO = 13
which give us
- JK = NJ+KN = 32+19 = 51
- KL = KO+LO = 19+13 = 32
- JL = MJ+LM = 32+13 = 45
Therefore, the perimeter of triangle JLK is:
JK+KL+JL = 51+32+45 = 128 units