In triangle PQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD?
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Using the cosine rule: Triangle PQR
30^2 = 50^2 + 36^2 – 2x50x36 Cos R
Cos R = (30^2 - 50^2 - 36^2)/ – 2x50x36
Cos R = 0.8044
R = 36.45
Using the cosine rule: Triangle PDR
PD^2 = 50^2 + 16^2 – 2x50x16 Cos 36.45
PD^2 = 1469
PD = 38.33
The centroid divides each median in the ratio 2:1
CD = 1/3 x 38.33
= 12.78
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Answer:
Step-by-step explanation:
Using the cosine rule: Triangle PQR
30^2 = 50^2 + 36^2 – 2x50x36 Cos R
Cos R = (30^2 - 50^2 - 36^2)/ – 2x50x36
Cos R = 0.8044
R = 36.45
Using the cosine rule: Triangle PDR
PD^2 = 50^2 + 16^2 – 2x50x16 Cos 36.45
PD^2 = 1469
PD = 38.33
The centroid divides each median in the ratio 2:1
CD = 1/3 x 38.33
= 12.78
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