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,
- If the medians of a triangle intersect each other at a point, it's Centroid of the triangle.
- 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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