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Semmy [17]
3 years ago
10

In Triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0

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 = \frac{1}{2} XZ

∵ XZ = 18 units

- Substitute the value of XZ in AB

∴ AB = \frac{1}{2} × 18 = 9 units

∵ B is the mid point of YZ

∵ C is the mid point of XZ

∴ BC = \frac{1}{2} XY

∵ AY = 7 units

∵ AY = \frac{1}{2} XY

∴ XY = 2 × AY

∴ XY = 2 × 7

∴ XY = 14 units

∴ BC = \frac{1}{2} × 14 = 7 units

∵ A is the mid point of XY

∵ C is the mid point of XZ

∴ AC = \frac{1}{2} YZ

∵ BZ = 8 units

∵ BZ = \frac{1}{2} YZ

∴ YZ = 2 × BZ

∴ YZ = 2 × 8

∴ YZ = 16 units

∴ AC = \frac{1}{2} × 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

#LearnwithBrainly

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