Answers:
- AE = 26
- AN = 58
- CT = 22.5
- Perimeter of triangle AEN = 127
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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
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We'll use the same idea to find AN
CP = (1/2)*AN
2*CP = AN
AN = 2*CP
AN = 2*29
AN = 58
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And we can also say,
CT = (1/2)*EN
CT = (1/2)*43
CT = 22.5
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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
