Given:
Point F,G,H are midpoints of the sides of the triangle CDE.
![FG=9,GH=7,CD=24](https://tex.z-dn.net/?f=FG%3D9%2CGH%3D7%2CCD%3D24)
To find:
The perimeter of the triangle CDE.
Solution:
According to the triangle mid-segment theorem, the length of the mid-segment of a triangle is always half of the base of the triangle.
FG is mid-segment and DE is base. So, by using triangle mid-segment theorem, we get
![\dfrac{1}{2}DE=FG](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7DDE%3DFG)
![DE=2(FG)](https://tex.z-dn.net/?f=DE%3D2%28FG%29)
![DE=2(9)](https://tex.z-dn.net/?f=DE%3D2%289%29)
![DE=18](https://tex.z-dn.net/?f=DE%3D18)
GH is mid-segment and CE is base. So, by using triangle mid-segment theorem, we get
![\dfrac{1}{2}CE=GH](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7DCE%3DGH)
![CE=2(GH)](https://tex.z-dn.net/?f=CE%3D2%28GH%29)
![CE=2(7)](https://tex.z-dn.net/?f=CE%3D2%287%29)
![CE=14](https://tex.z-dn.net/?f=CE%3D14)
Now, the perimeter of the triangle CDE is:
![Perimeter=CD+DE+CE](https://tex.z-dn.net/?f=Perimeter%3DCD%2BDE%2BCE)
![Perimeter=24+18+14](https://tex.z-dn.net/?f=Perimeter%3D24%2B18%2B14)
![Perimeter=56](https://tex.z-dn.net/?f=Perimeter%3D56)
Therefore, the perimeter of the triangle CDE is 56 units.
Answer:
24
Step-by-step explanation:
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Answer:
y = 10
x = 64
Step-by-step explanation:
the equations containing y are adjacent angles in a parallelogram, meaning that they are supplementary, so we can create an equation:
5y + 2 + 12y + 8 = 180
solve this to get y = 10
the equation for x would be 2x + 5y + 8 = 180 because these angles are also supplementary
solve this to get x = 64