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30 In AXYZ shown below, medians XE, YF, and ZD intersect at C.
If CE = 5, YF = 21, and XZ = 15, determine and state the perimeter of triangle CFX.

Respuesta :

Answer: 24.5

Step-by-step explanation:

So you have to remember that some sections are broken into medians so you have a 2:1 ratio in some areas. So XZ is 15 right, so you'd have to divide that section by 2 to get 7.5 for XY and FZ. Next FY is split into a 2 to 1 ratio with the YC being the larger one part to that would be the 2 and the FC being the smaller part to it's 1, so you'd divide the 21 using the 2:1 so FC would be 7 and YC would be 14. Lastly, there's XE. So XE would be split into a 2:1 ratio having the XC being the bigger part so it would be 2 and CE being the smaller part to it would be 1. So XC is 10 and CE is 5.

So now add together 7.5+7+10 to get the answer 24.5

Hope that helped :)

Given question is incomplete; find the complete question in the attachment.

 Perimeter of ΔCFX will be [tex]24.5[/tex] units.

   Given in the question,

  • ΔXYZ with medians XE, YF and ZD intersecting at a point C.
  • CE = 5, YF = 21 and XZ = 15

Property of Centroid of a triangle,

  1. If the medians of a triangle intersect each other at a point, it's Centroid of the triangle.
  2. Centroid divides the median in the ratio of 2 : 1.

In ΔXYZ,

Point C will divide the median YF in the ratio of 2 : 1.

Therefore, CY : CF = 2 : 1

And measure of CF = [tex]\frac{1}{1+2}\times (FY)[/tex]

                                 = [tex]\frac{1}{3}\times 21[/tex]

                                 = [tex]7[/tex] units

Similarly, point C will divide another median XE in the same ratio of 2 : 1,

CX : CE = 1 : 1

[tex]\frac{CX}{CE}=\frac{2}{1}[/tex]

[tex]\frac{CX}{5}=\frac{2}{1}[/tex]

[tex]CX=10[/tex] units

Since, F is the midpoint of side XZ,

XF = [tex]\frac{15}{2}=7.5[/tex] units

Perimeter of ΔCFX = CF + FX + CX

                               = [tex]7+7.5+10[/tex]

                               = [tex]24.5[/tex] units

    Therefore, perimeter of ΔCFX will be [tex]24.5[/tex] units.

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https://brainly.com/question/4421837

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