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jessycawest15
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5 lb book chapter 27 #42

by jessycawest15 Mon Sep 08, 2014 10:00 am

Hello. Could you please explain how to derive to the answer for this problem because the explanation is unclear. Thank you for your time.
-Jessyca
tommywallach
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Re: 5 lb book chapter 27 #42

by tommywallach Mon Sep 08, 2014 9:11 pm

Hey Jessyca,

BE and AC are the height and base of the triangle.

BC and AD are also the height and base of the triangle.

(Every triangle has three bases, because you could put any of the three sides "flat" on the ground. Thus every triangle also has three heights, because a height is a line drawn from a vertex to the opposite base that meets it at a 90-degree angle.)

Because 1/2bh is the area, and both of these "bh" represent the same triangle, the two columns must be equal.

Hope that makes more sense!

-t
jessycawest15
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Re: 5 lb book chapter 27 #42

by jessycawest15 Mon Sep 22, 2014 6:41 pm

I want to be clear about this matter. So you are saying that AC is the height as well as the base?
tommywallach
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Re: 5 lb book chapter 27 #42

by tommywallach Fri Sep 26, 2014 10:21 pm

Hey Jessica,

Imagine a triangle. You can see the base at the bottom. The height is defined as a line drawn from the highest point to the base that meets the base (or a horizontal extension of the base, if the peak of the triangle isn't over the base) at a ninety-degree angle.

Now imagine that you turned that triangle so that one of the OTHER sides was the base. There is now a new height. However, base*height will always be the same (because the area of a triangle is 1/2 * b * h, and the area of the triangle wouldn't change just because you turned it around).

See what I mean? Every triangle has three possible bases, and each of those bases comes with its own height.

-t