contestada

$\triangle DEF$ 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

Respuesta :

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 20

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

The perimeter of ΔABC = 20

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