sorry for the scribbles
Thank you!!!
GRE Forum Archive
4 postsPage 1 of 1
- ben.chantana
- Students
- Posts: 4
- Joined: Sun Oct 07, 2012 5:01 am
Geometry problem help please
Last edited by ben.chantana on Mon Oct 08, 2012 1:32 am, edited 1 time in total.
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Geometry problem help please
Hey Ben,
If this is from the Official Guide, I'm not sure it's legal to post it up here, just FYI. Also, you didn't print the whole thing. But I'm happy to talk about the part that you did print!
The easiest way to do this question is to recognize that, because these are similar triangles (CDE and FGA), they have all the same angles. This means that we can just divide the big triangle up into little triangles. Triangle CDE fits into the quadrilateral below it three times, and into the one below that 5 times (try drawing it, dividing both shapes into triangles, and you'll see what I mean). This means the whole triangle is made up of 9 triangles the size of CDE, so you can simply multiply 42 by 9 to get the answer.
If you're not going to do it that way you can simply notice that the big triangle has 3 times the height of the small triangle (DE = EF = EG, by definition), and 3 times the base (CE = 1/2 BF = 1/4 AG). So the area of the big triangle will be 9 times (3 * 3) the area of the small triangle.
Let me know if that makes sense!
-t
If this is from the Official Guide, I'm not sure it's legal to post it up here, just FYI. Also, you didn't print the whole thing. But I'm happy to talk about the part that you did print!
The easiest way to do this question is to recognize that, because these are similar triangles (CDE and FGA), they have all the same angles. This means that we can just divide the big triangle up into little triangles. Triangle CDE fits into the quadrilateral below it three times, and into the one below that 5 times (try drawing it, dividing both shapes into triangles, and you'll see what I mean). This means the whole triangle is made up of 9 triangles the size of CDE, so you can simply multiply 42 by 9 to get the answer.
If you're not going to do it that way you can simply notice that the big triangle has 3 times the height of the small triangle (DE = EF = EG, by definition), and 3 times the base (CE = 1/2 BF = 1/4 AG). So the area of the big triangle will be 9 times (3 * 3) the area of the small triangle.
Let me know if that makes sense!
-t
- ben.chantana
- Students
- Posts: 4
- Joined: Sun Oct 07, 2012 5:01 am
Re: Geometry problem help please
Oops, I will remove the image then.
It makes sense now. I didn't know that we can conclude that DE=EF=FG
Thank you!
It makes sense now. I didn't know that we can conclude that DE=EF=FG
Thank you!
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Geometry problem help please
Hey Ben,
The key is to realize that both the small triangle and the big triangle are similar (they have 90 degree angles at the bottom, and the same top angle, so the third angle must be the same as well). This means that they are in direct proportion. So if the hypotenuse of the big triangle is three times as big as the hypotenuse of the little triangle, that means all the sides are in a ratio of 1:3.
Glad to help!
-t
The key is to realize that both the small triangle and the big triangle are similar (they have 90 degree angles at the bottom, and the same top angle, so the third angle must be the same as well). This means that they are in direct proportion. So if the hypotenuse of the big triangle is three times as big as the hypotenuse of the little triangle, that means all the sides are in a ratio of 1:3.
Glad to help!
-t
4 posts Page 1 of 1