Answer:
4a. See attached.
4b. 32
6. x = 4.5, LM = 7.5, LN = 10.5
Step-by-step explanation:
4b. The midline of a triangle is half the length of the baseline it is parallel to. Hence the segment FH is twice the length of CD, or 2·16 = 32.
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6. The angle bisector MP divides the triangles segments so those on one side of it are proportional to corresponding ones on the other side of it. Here, that means ...
x/(x+3) = 6/10
10x = 6x + 18 . . . . multiply by 10(x+3)
4x = 18 . . . . . . . . . subtract 6x
x = 4.5 . . . . . . . . . divide by 4
Then segment LM is x+3 = 4.5+3 = 7.5, and LN = x+6 = 4.5+6 = 10.5.
The blanks are filled as ...
x = 4.5 LM = 7.5 LN = 10.5
