Calculating Mean Proportional Between 36 and 81
The mean proportional (or geometric mean) between two numbers, say a and b, is a number x such that the ratio a : x is equal to the ratio x : b. Mathematically, this is represented as:
\( \frac{a}{x} = \frac{x}{b} \)
This can be rewritten as:
\( x^2 = a \times b \)
Therefore, the mean proportional x is the square root of the product of the two numbers:
\( x = \sqrt{a \times b} \)
Step-by-Step Calculation
- Identify the two numbers given: a = 36 and b = 81.
- Substitute these values into the formula for the mean proportional:
\( x = \sqrt{36 \times 81} \)
- Calculate the product of the two numbers:
\( 36 \times 81 = 2916 \)
- Find the square root of the product:
\( x = \sqrt{2916} \)
Alternatively, calculate the square root of each number first:
\( x = \sqrt{36} \times \sqrt{81} \)
\( x = 6 \times 9 \)
- The result is the mean proportional:
\( x = 54 \)
The mean proportional between 36 and 81 is 54.
Similar Questions
A father distributed two different amounts among his sons P, Q, R and S. First amount was distributed in the ratio 5 : 4 : 3 : 2 and the second amount was distributed in the ratio 6 : 7 : 8 : 9. If the second amount is thrice the first amount, then which son will get the maximum amount?
A sum of ₹420 is divided among A, B, C, and D such that: A : B = 4 : x, B : C = x : 7, C : D = 6 : (x − 3). If B and C together get ₹210, find the value of x.
Given the ratio 3:4::6:8, which operation verifies the proportion?
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P, Q and R are three batsmen. The ratios of runs scored by them in a certain match were as follows:
P : Q = 5 : 7 and Q : R = 2 : 3.
If they scored a total of 765 runs, then find the number of runs scored by R.- If ₹ 87 was divided between James and Radha in the ratio 1 : 2, how much money did Radha get?
- If 3 dozen guavas cost ₹ 90, how many guavas can be bought for ₹ 240?
Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
The average of the areas of 2 similar triangles is 706.5 m2 whose perimeters are in the ratio of 6 : 11. What is 20% of the difference (in m2) in areas of both triangles?
In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
