Answer:
Explanation:
We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.
We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.
Now, we can use the Pythagorean theorem to find the length of the third side, LM:
LM^2 = LT^2 + TM^2
LM^2 = 9^2 + 16^2
LM^2 = 337
LM = sqrt(337)
Therefore, the perimeter of triangle LMO is:
LM + MO + LO = sqrt(337) + 2(12) + 32
Perimeter = sqrt(337) + 56
To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:
TP^2 = TJ^2 + JP^2
TP^2 = 18^2 + 24^2
TP^2 = 900
TP = 30
Therefore, the perimeter of triangle TJP is:
TJ + JP + TP = 18 + 24 + 30
Perimeter = 72
Therefore, the perimeter of triangle TJP is 72.