Question

Given that LM is a midsegment of IJK, find JK.
A. 7
B. 8
C. 14
D. 16

Answer 1

16

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.

Answer 2

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