Answer:
Distance of midpoints of the segments AB and CD is 24 cm.
Step-by-step explanation:
Given that
AD = 36 cm
Points C and B are in segment AB.
The ratio of distance AB:BC:CD = 2:3:4
To find:
Distance of midpoints of the segments AB and CD ?
Solution:
The ratio of distance AB:BC:CD =2:3:4
Let AB = [tex]2x[/tex]
Let BC = [tex]3x[/tex]
Let CD = [tex]4x[/tex]
Now, it is clear that AD = AB + BC + CD
[tex]\Rightarrow 36=2x+3x+4x\\\Rightarrow 36=9x\\\Rightarrow x = 4\ cm[/tex]
Putting the value of x to find AB, BC and CD:
AB = [tex]2\times 4 = 8\ cm[/tex]
BC = [tex]3\times 4 = 12\ cm[/tex]
CD = [tex]4 \times 4 = 16\ cm[/tex]
Now, mid point of AB will be [tex]\frac{8}2 = 4\ cm[/tex] on the right side of point A.
And
mid point of CD will be [tex]\frac{16}2 = 8\ cm[/tex] on the left side of point D.
[tex]\therefore[/tex] If we subtract 4 and 8 from AD we will get distance between mid points of segments AB and CD.
So, Distance of midpoints of the segments AB and CD = 36 - 4 -8 = 24 cm.
Distance of midpoints of the segments AB and CD is 24 cm.
