Question: 3 Triangles

The enlargement factor of the isosceles triangle can be written in several equivalent ways.
In the video, we say the enlargement factor = 6/√2, but we don't bother about simplifying that value, since we're not asked to find that specific value.
Rather, we're just going to use it to find the other lengths in the triangle.

In actuality, 6/√2 = 3√2 = √18. They all have the exact same value. Here's why:
Take: 6/√2
Multiply top and bottom by √2 to get: (6√2)/2
Simplify to get: 3√2
So, 6/√2 = 3√2

Now take: 3√2
Rewrite 3 as √9 to get: (√9)(√2)
Simplify to get: √18

So, the enlargement factor of the isosceles triangle = 6/√2 = 3√2 = √18

We're told that AD = BD in the given information, which means triangle ABD is an isosceles triangle with TWO angles measuring 45 degrees each.

So, once we conclude that side BD = 6/√2, we can also conclude that side AD = 6/√2, since we are told that AD = BD in the given information.

However, since the given information also tells us that side AB = 6, we can't have the say that all three sides of triangle ABD have length 6/√2.