Question

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

Answer 1

The perimeter of triangle ABC is 24 units

Step-by-step explanation:

There is a fact in any triangle, the segment joining the mid points of

two sides of the triangle is:

• Parallel to the third side
• Its length is half the length of the third side

In Δ XYZ

∵ A is the mid point of XY

∵ B is the mid point of YZ

∴ AB = $\frac{1}{2}$ XZ

∵ XZ = 18 units

∴ AB = $\frac{1}{2}$ × 18 = 9 units

∵ C is the mid point of XZ

∵ B is the mid point of YZ

∴ BC = $\frac{1}{2}$ XY

∵ AY = 7 units

∵ AY = $\frac{1}{2}$ XY

∴ 7 = $\frac{1}{2}$ XY

- Multiply both sides by 2

∴ 14 = XY

∴ 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

∴ 8 = $\frac{1}{2}$ YZ

- Multiply both sides by 2

∴ 16 = YZ

∴ AC = $\frac{1}{2}$ × 16 = 8 units

∵ The perimeter of any triangle is 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/10677255

#LearnwithBrainly