Posted by **Danyoline** on Wednesday, December 29, 2010 at 9:31pm.

In triangle ABC, DE is parallel to AB. If DE is one-fifth AB, what is the ratio of the area of triangle DEC to the area of triangle ABC?

- geometry -
**Damon**, Wednesday, December 29, 2010 at 9:54pm
for any similar figures the ratio of areas is the square of the ratio of lengths.

so

1/25

You can easily prove this for yourself by noting that if DE = AB/4

Then the altitude of the little triangle = 1/5 the altitude of the big triangle

(1/2)(1/5)(1/5) = (1/25) * (1/2) (1)(1)

- geometry -
**Damon**, Wednesday, December 29, 2010 at 10:00pm
by the way, for similar SOLID 3 d figures:

areas are proportional to square of length ratio

Volumes are proportional to CUBE of scale ratio

This is handy to use for quick estimates

For example compare a 500 foot long oil tanker to a similar 1000 foot tanker

the big one has 2^2 = 4 times the surface area in the water

however it is 2^3 = 8 times the volume and therefore cargo capacity.

The water resistance is roughly proportional to area

so it carries 8 times the oil with 4 times the drag

so it carries twice as much oil per horsepower for the same speed.

That is why ships keep getting bigger and bigger.

- typo -
**Damon**, Wednesday, December 29, 2010 at 10:01pm
You can easily prove this for yourself by noting that if DE = AB/"5" **not four**

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