Question

What is JK? please explain/show your work on how you got your answer​

Answer 1

• JK = 20 m

Explanation:

• A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
• A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side.

Point J is midpoint of side HI as HJ = JI

Point K is midpoint of side GI as GK = KI

JK is midsegment as connects the midpoints of the sides

JK = 1/2HG as per property of midsegment

• 6x - 4 = 10x/2
• 6x - 4 = 5x
• 6x - 5x = 4
• x = 4

JK = 6x - 4 = 6*4 - 4 = 24 - 4 = 20 m

Answer 2

`JK=20m`

Explanation:

It is given in the diagram that IJ = JH and IK = KG. Therefore, by the definition of a midpoint, we know that J and K are the midpoints of segments IH and IG respectively. Then, it can be concluded that JK is a midsegment by the definition of a midsegment. The Midsegment Theorem states that a midsegment connecting the midpoints of two sides of a triangle is parallel and half of the length of the third side. Thus, we know that JK is half of HG. Now, we can set up the following equation to solve for x:

`JK = (1)/(2)HG\\6x-4=(1)/(2)(10x)`

Solving for x, we get:

`6x-4=(1)/(2)(10x)\\6x-4=5x\\x-4=0\\x=4`

Therefore,
`JK = 6x - 4 = 6(4) - 4=24-4=20 m`.

Hope this helps!