SOLUTION: The vectors (8,0) and (3,4) form a paralellogram. Find the lengths of its altitudes. I don't know how to generate the algebraic equations to solve this one.

Question 149699: The vectors (8,0) and (3,4) form a paralellogram. Find the lengths of its altitudes. I don't know how to generate the algebraic equations to solve this one.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First plot the two points (0,0) and (3,4). Now draw a right triangle with the hypotenuse that goes through the two points. With the use of pythagoreans theorem, we find that the hypotenuse is 5 units (since ). So our drawing looks like this:

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Now if draw the vectors and draw the parallelogram, we can see that the height of the parallelogram is the y-coordinate of the point (3,4). So the first height is 4.

Photobucket - Video and Image Hosting

So from the drawing, we see that the base is 8 units and the height is 4 units.

Now if we compute the area, we get:

Now let the vector from (0,0) to (3,4) be the new base. So the base is now 5. The area is still 32. So this means that

Solving for h, we get

So the second height is 6.4
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