Final answer:
The value of x in the midsegment problem, where HJ is the midsegment and GK is the side of the triangle, is found to be 36 by setting up the equation HJ = 1/2 GK and solving for x.
Step-by-step explanation:
To solve for x in the midsegment of a triangle problem, we need to apply the properties of a midsegment. A midsegment of a triangle is a segment connecting the midpoints of two sides, and its length is half the length of the third side. In this case, HJ is the midsegment, and it is equal to x, and GK is the third side of the triangle and equal to x + 36.
Since HJ is a midsegment, we can set up the equation:
HJ = ½ GK
Substituting the given lengths, we get:
x = ½ (x + 36)
Now we can solve this equation for x:
- Multiply both sides of the equation by 2 to get rid of the fraction:2x = x + 36
- Subtract x from both sides of the equation to find the value of x:x = 36
Therefore, the length of HJ and the value of x is 36.