Find the mean proportional between 25 and 81.
45
To find the mean proportional between two numbers, we set up the equation for the geometric mean: if \( a \) and \( b \) are the two numbers, the mean proportional \( x \) is such that:
\( x^2 = a \cdot b \)
Given \( a = 25 \) and \( b = 81 \), we substitute these values into the equation:
\( x^2 = 25 \cdot 81 \)
\( x^2 = 2025 \)
To find \( x \), take the square root of both sides:
\( x = \sqrt{2025} \)
Calculation:
\(\sqrt{2025} = 45\)
Thus, the mean proportional between 25 and 81 is 45.
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:
8 apples and 10 oranges weigh 5 kg. 12 apples and 20 oranges weigh 9 kg. What is the weight (in kg, rounded off to the nearest integer) of 15 apples and 24 oranges?
