Finding Mean Proportional Between 49 and 64
The mean proportional (or geometric mean) between two numbers, a and b, is a value x such that the ratio a:x is equivalent to the ratio x:b. This relationship can be written as:
\( \frac{a}{x} = \frac{x}{b} \)
Cross-multiplying gives:
\( x^2 = a \times b \)
To find the mean proportional, we take the square root of the product of the two numbers:
\( x = \sqrt{a \times b} \)
Calculation Steps
For the given numbers 49 and 64:
- Identify the numbers: \(a = 49\) and \(b = 64\).
- Apply the mean proportional formula: \(x = \sqrt{49 \times 64}\).
- Calculate the square roots separately: \(\sqrt{49} = 7\) and \(\sqrt{64} = 8\).
- Multiply the results: \(x = 7 \times 8\).
- The mean proportional is \(x = 56\).
Thus, the mean proportional between 49 and 64 is 56.
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 = 5 : 7 and Q : R = 2 : 3.
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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.
