Equal Areas problem?

Question

I have a line of length 66 ft. on each side of the line there is a triangle. the triangle on top has twice the area of the triangle on the bottom. Both triangles are right triangles with slopes = -1576. how long are each triangle??? Oh, and the height of the top triangle minus the height of the little triangle = 104000

http://img221.imageshack.us/img221/9838/aaare3.png

Answer 1

The area of a triangle is 1/2 times base times altitude.

Let B1 and B2 be the bases and A1 and A2 be the altitudes.
We know that the bottom triangle (number 1) has half the area of the top triangle (number 2) so

2 * 1/2 * B1 * A1 = 1/2 * B2 * A2

which simplifies to

2 B1 A1 = B2 A2

You also know that

B1 + B2 = 66

and that

A2 - A1 = 10400

You are also given a slope of 1576. Slope = rise / run = altitude / base so you know that

A1 / B1 = A2 / B2 = 1576.

You now have enough information to solve for A1, A2, B1, B2, and the two areas. Enjoy!