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

Question

2 years ago

11

perimeter of $\triangle XYZ$ is $5$, what is the perimeter of $\triangle ABC

1 answer:

lbvjy [14] · Answer 1 · 2022-10-13T14:37:02+03:00

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.

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: