AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD. HELP ASAP PLZ will give brainiest if u get it right!

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 =

Let BC =

Let CD =

Now, it is clear that AD = AB + BC + CD

Putting the value of x to find AB, BC and CD:

AB =

BC =

CD =

Now, mid point of AB will be on the right side of point A.

And

mid point of CD will be on the left side of point D.

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.