Manhattan Prep Geo p. 66 #11

[Alexander]

Hi -

I have no idea whats going on in this problem, and the explanation isn't very clear.

- I understand how to get the area of the bolded triangle = 12*3/2 = 18

- How do you solve for the unknown height? The explanation shows: 7*X = 36

- Is this saying that 7 (base of the bolded triangle) * some height = area of the bolded triangle? We already have a height in the bolded triangle (3).

On the bottom of p. 52 of the geo prep book, the idea of 'heights' and 'bases' outside the triangle is discussed and its quite confusing!

Thanks,
Alexander

I'm having trouble conceptually and thought I'd post.

Thanks,
Alexander

[tommywallach]

Hey Alexander,

Let's talk concepts.

Every triangle has 3 bases. Any side can be a base (just spin the page around!). But whichever side you are considering the base creates a new height. The definition of the height is as follows:

Draw a line from the apex of the triangle down to either the base or the horizontal extension of the base, that meets that base (or extension) at a 90 degree angle.

In the case of this triangle, we could consider the base of the triangle 12 and the height 3.

We could ALSO consider the base 7. If we do that, the height is now x, because that dotted line represents what I described as the height: it is a line drawn from the apex of the triangle (that point up there is the highest point if you look at this triangle with the 7 line horizontal on the bottom) to the EXTENSION of the base line.

Obviously, no matter which base/height combo you choose, the area of the triangle has to be the same. We already know this triangle has an area of 18, so (7 * x)/2 = 18 as well.

Does that help?

-t