Question: 3 Triangles

Comment on 3 Triangles

Why is the enlargement factor of the isosceles triangle not root18?
Root18 times root2 = 6.
gmat-admin's picture

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

gmat-admin's picture

How would you then solve the enlargement factor for the second (30-60-90) triangle using "root 18" as side BD?

gmat-admin's picture

Side BC has length √18.
The corresponding side of the base 30-60-90 triangle has length 2
So, the enlargement factor = (√18)/2

If we wish, we can simplify (√18)/2

√18 = (√9)(√2) = 3√2
So, the enlargement factor = (3√2)/2

Please note that (√18)/2 = (3√2)/2 = 6/√2


Perfectly used 1x:1x:sqrt(2)x and 1x:sqrt(3)x:2x

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