What is the ratio of mean proportional between 3.6 and 12.1 and the third proportional between 2 and 11?
What is the ratio of mean proportional between 3.6 and 12.1 and the third proportional between 2 and 11? Correct Answer 6 ∶ 55
Let the Mean proportional between 3.6 and 12.1 be x
From the definition of mean proportion
3.6 ∶ x ∶∶ x ∶ 12.1
3.6/x = x/12.1
x2 = 3.6 × 12.1
x = √(3.6 × 12.1) = √(36 × 121)/100 = (6 × 11)/10
Let the third proportional of 2 and 11 be y, then definition of third proportion
2 ∶ 11 ∶∶ 11 ∶ y
2/11 = 11/y
y = (11 × 11)/2 = 121/2
Required ratio = (6 × 11)/10 ∶ 121/2 = 6 ∶ 55
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Feb 20, 2025