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Vsevolod [243]
3 years ago
11

$\triangle DEF$ is the medial triangle of $\triangle ABC$ and $\triangle XYZ$ is the medial triangle of $\triangle DEF.$ If the

perimeter of $\triangle XYZ$ is $5$, what is the perimeter of $\triangle ABC
Mathematics
1 answer:
lbvjy [14]3 years ago
6 0

A medial triangle is made from the midlines of the larger triangle, and its

length is half the length of the third side of the triangle.

  • The perimeter of ΔABC is <u>20</u>

Reasons:

The medial triangle of triangle ΔABC is triangle ΔDEF

The medial triangle of  ΔDEF is ΔXYZ

The perimeter of ΔXYZ = 5

By the midpoint theorem, we have;

The lengths of the sides of ΔDEF = 0.5 × The lengths of the sides of ΔABC

∴ The perimeter of ΔDEF = 0.5 × The perimeter of ΔABC

Which gives;

The perimeter of ΔABC = 2 × The perimeter of ΔDEF

Similarly, between ΔXYZ and ΔDEF, we have;

The perimeter of ΔDEF = 2 × The perimeter of ΔXYZ

∴ The perimeter of ΔDEF = 2 × 5 = 10

Therefore;

The perimeter of ΔABC = 2 × 10 = 20

<u>The perimeter of ΔABC = 20</u>

Learn more about the perimeter of a triangle here:

brainly.com/question/1340753

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