ACT Math 2.2 Plane Geometry
ACT Math: Plane Geometry Drill 2, Problem 2. What is the perimeter of triangle GHF?
|ACT Math||Plane Geometry|
|ACT Mathematics||Plane Geometry|
|Foreign Language||Arabic Subtitled|
Properties of plane figures
The concept of proof and proof techniques
|Product Type||ACT Math|
Yeah. Well -- FGH and FDE are SIMILAR triangles -- that is, all their angles are equal, and
GH is parallel to DE.
How do we know? Well, since the two triangles are SIMILAR, it means that the perimeter edges
Start by finding the perimeter of triangle FDE...
We get 8 plus 2 plus 6 plus 2 plus 8... which is 26.
We want to find GH and we know that GH is proportional to DE.
So we can write FG is to FD, or 8 is to 10, as GH is to DE -- and DE is 6... so we get
the ratio 8 is to 10 as GH is to 6.
Cross-multiply and we get 48 equals 10 times GH... so the distance GH is 48 over 10...
Now we have to just add the perimeter sides of 8 and 8 which is 16; add to 4.8 and we
get 20.8 as the perimeter for triangle GHF.