ABCD IS A TRAPEZIUM SUCH THAT AB IS PARALLEL TO EF & CD. IF E IS THE MIDPOINT OF AD , AB =3CM AND CD=5CM, FIND EF.

EF is the average of the two base lengths: (AB+CD)/2

To find the length of EF, we can use the property of trapezium where the length of the parallel sides is proportional to the length of the base.

First, let's draw a diagram to visualize the given information:

A_____________B
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E|____________|F
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D_____________C

Given:
AB = 3 cm
CD = 5 cm
E is the midpoint of AD

Since E is the midpoint of AD, we can infer that AE = ED. Let's call it 'x'.
So, AE = ED = x cm

Now, we can see that the trapezium can be divided into two triangles, AEF and EFC, by drawing a line segment EF.

AEF and EFC are similar triangles because their corresponding angles are equal (since AB is parallel to EF).

Using the property of similar triangles, we can write the proportion:

EF / AB = FC / CD

Substituting the given values:
EF / 3 = FC / 5

Since FC = CD - EF (as AB is parallel to EF),
EF / 3 = (5 - EF) / 5

Cross multiplying, we get:
EF * 5 = 3 * (5 - EF)

Expanding, we get:
5EF = 15 - 3EF

Combining like terms, we have:
8EF = 15

Dividing by 8 on both sides, we get:
EF = 15 / 8

Therefore, EF = 1.875 cm.