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Answer: Option D. 16
Solution:
If LM is a midsegment of IJK, it is joining the midpoint of the sides IJ and IK, and it's half the length of the base of the triangle (JK), then:
L is the midpoint of the side IJ, and divides it into two congruent parts:
IL=LJ
Replacing IL by 7x and LJ by 3x+4:
7x=3x+4
Solving for x: Subtracting 3x both sides of the equation:
7x-3x=3x+4-3x
Subtracting:
4x=4
Dividing both sides of the equation by 4:
4x/4=4/4
Dividing:
x=1
Then we can determine the length of LM:
LM=2x+6
Replacing x by 1 in the equation above:
LM=2(1)+6
LM=2+6
LM=8
and because LM is half the length of the base of the triangle (JK)
LM=(1/2) JK
Replacing LM by 8:
8=(1/2) JK
Multiplying both sides of the equation by 2:
2(8)=2(1/2) JK
16=(2/2) JK
16=(1) JK
16=JK
JK=16
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Rewritten by : Barada
Answer:
16
Step-by-step explanation:
We know that segment LM is the mid-segment of the triangle IJK which means ILM is half the size of IJK.
So, IL = LJ.
We know that IL = 7x and LJ = 3x+4 so putting these values equal to each to find the value of x:
7x = 3x + 4
7x - 3x = 4
x =4/4
x = 1
Now, if x = 1, then the segment LM will be:
2x + 6 = 2(1) + 6 = 8
If LM is half the length of JK, then JK is two times the length og LM.
Therefore, JK = 2 * 8 = 16.
