Question

4) If C, P, and T are the midpoints of the sides

Answer 1

Answers:

• AE = 26
• AN = 58
• CT = 22.5
• Perimeter of triangle AEN = 127

=========================================================

Work Shown:

Because points C, P, and T are midpoints of the sides of triangle AEN, this means the segments CP, PT, and CT are midsegments of triangle AEN.

The segment PT = 13 is a midsegment of the larger triangle, and it is parallel to the side AE. Recall the midsegment is half as long as its parallel side.

This means,

PT = (1/2)*AE

2*PT = AE

AE = 2*PT

AE = 2*13

AE = 26

---------------

We'll use the same idea to find AN

CP = (1/2)*AN

2*CP = AN

AN = 2*CP

AN = 2*29

AN = 58

---------------

And we can also say,

CT = (1/2)*EN

CT = (1/2)*43

CT = 22.5

----------------

Add up the sides of triangle AEN to find its perimeter

Perimeter of triangle AEN = (AE)+(EN)+(AN)

Perimeter of triangle AEN = (26)+(43)+(58)

Perimeter of triangle AEN = 127