Question

Given that B, C, and D are the midpoints of ZYA, find the perimeter of ZYA.
A. 70.6
B. 72.6
C. 76.6
D. 77.6

Answer 1

D. 77.6 just add everything together and multiply by 2

Answer 2

Answer:

D. 77.6

Step-by-step explanation:

We have been given a triangle ZYA in which B, C, and D are the midpoints. We are asked to find the perimeter of triangle ZYA.

We will triangle mid-segment theorem to solve our given problem.

The triangle mid-segment theorem states that the segment joining midpoints of two sides of a triangle is parallel to 3rd side and half the measure of parallel side.

$\text{Measure of side YA}=2\times BD$

$\text{Measure of side YA}=2\times 11.1$

$\text{Measure of side YA}=22.2$

$\text{Measure of side YZ}=2\times CD$

$\text{Measure of side YZ}=2\times 13.7$

$\text{Measure of side YZ}=27.4$

$\text{Measure of side ZA}=2\times CB$

$\text{Measure of side ZA}=2\times 14$

$\text{Measure of side ZA}=28$

$\text{Perimeter of triangle ZYA}=22.2+27.4+28$

$\text{Perimeter of triangle ZYA}=77.6$

Therefore, the perimeter of triangle ZYA is 77.6 units.