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**

## Answer this Question

## Related Questions

- Geometry - Given: X, Y, and Z are the midpoints of teh sides of triangle ABC. ...
- math - B . . . . . . . . . . . . . . C A Triangle ABC is right angled at A. The...
- sanket study centre - In triangle ABC p,q,r such that they lie interior of ...
- Geometry - Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are...
- Math - In triangle ABC, D bisects side BC, G bisects side AB, and the points E ...
- Math - In triangle ABC, D bisects side BC, G bisects side AB, and the points E ...
- geometry - Open that link please please help me with my assignments 1. in the ...
- Math please help urgent - In triangle ABC, D bisects side BC, G bisects side AB...
- geometry - right triangle ABC with right angle C, AC=22 and BC=6, altitude CD ...
- 9th grade - given that a(-1,8) ,b(2,4) and if the line y=4 is the axis of ...

More Related Questions