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

D. 77.6

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* BD`

`\text{Measure of side YA}=2* 11.1`

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

`\text{Measure of side YZ}=2* CD`

`\text{Measure of side YZ}=2* 13.7`

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

`\text{Measure of side ZA}=2* CB`

`\text{Measure of side ZA}=2* 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.