If K is the midpoint of JL. JK = 5x+17 and
KL = 8x-31, find JL.
Since K is the midpoint of JL, the lengths of JK and KL should be equal.
Given that:
JK = 5x + 17
KL = 8x - 31
Setting them equal to each other:
5x + 17 = 8x - 31
Rearranging the equation:
-3x = -48
Solving for x:
x = (-48)/(-3) = 16
Substituting this value back into either equation to find JL:
JL = JK = 5x + 17 = 5(16) + 17 = 80 + 17 = 97
To find JL, we need to find the length of JK and KL, and then add them together.
Given:
JK = 5x + 17
KL = 8x - 31
Since K is the midpoint of JL, the lengths JK and KL must be equal. So, we can set up an equation:
JK = KL
5x + 17 = 8x - 31
Now, let's solve for x.
Subtract 5x from both sides:
17 = 3x - 31
Add 31 to both sides:
48 = 3x
Divide both sides by 3:
16 = x
Now that we have x, we can substitute it back into one of the equations to find JL.
Let's substitute x = 16 into JK = 5x + 17:
JK = 5(16) + 17
JK = 80 + 17
JK = 97
Substitute x = 16 into KL = 8x - 31:
KL = 8(16) - 31
KL = 128 - 31
KL = 97
Finally, we can find JL by adding JK and KL:
JL = JK + KL
JL = 97 + 97
JL = 194
Therefore, JL is equal to 194.