The perimeter of triangle ABC is 24 units
Step-by-step explanation:
If a segment joining the mid points of two sides of a triangle, then
this segment is:
- Parallel to the third side
- Its length is half the length of the third side
In The triangle XYZ
∵ A is the mid point of XY
∵ B is the mid point of YZ
∴ AB = [tex]\frac{1}{2}[/tex] XZ
∵ XZ = 18 units
- Substitute the value of XZ in AB
∴ AB = [tex]\frac{1}{2}[/tex] × 18 = 9 units
∵ B is the mid point of YZ
∵ C is the mid point of XZ
∴ BC = [tex]\frac{1}{2}[/tex] XY
∵ AY = 7 units
∵ AY = [tex]\frac{1}{2}[/tex] XY
∴ XY = 2 × AY
∴ XY = 2 × 7
∴ XY = 14 units
∴ BC = [tex]\frac{1}{2}[/tex] × 14 = 7 units
∵ A is the mid point of XY
∵ C is the mid point of XZ
∴ AC = [tex]\frac{1}{2}[/tex] YZ
∵ BZ = 8 units
∵ BZ = [tex]\frac{1}{2}[/tex] YZ
∴ YZ = 2 × BZ
∴ YZ = 2 × 8
∴ YZ = 16 units
∴ AC = [tex]\frac{1}{2}[/tex] × 16 = 8 units
∵ The perimeter of a triangle = the sum of the lengths of its sides
∴ Perimeter Δ ABC = AB + BC + AC
∴ Perimeter Δ ABC = 9 + 7 + 8 = 24 units
The perimeter of triangle ABC is 24 units
Learn more:
You can learn more about triangles in brainly.com/question/5924921
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