Question

What is the length of BD?

Answer 1

The length is `BD=36cm`

Explanation:

Let the mid-point of `BC` be `=E`

Let the mid-point of `CD` be `=F`

Then,

`AG=2/3AE` and `AG'=2/3AF`

As `G` and `G'` divide `AE` and `AF` in the same ratio

The lines `GG'` and `BD` are parallel

We apply Thales' Theorem

`GG'=2/3EF`

`EF=3/2*12=18cm`

`BD=2*EF=2*18=36cm`