Advertisements
Advertisements
Question
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
Advertisements
Solution
Let a and b be the two numbers, whose mean proportional is 12.
∴ ab =122 ⇒ ab = 144 ⇒ b = `144/"a"` ...........(i)
Now, third proportional is 324
∴ a : b : : b : 324
⇒ `(144/"a")^2 = 324 "a"`
⇒ `(144)^2/"a"^2 = 324 "a"`
⇒ a3 = `(144 xx 144)/324`
⇒ a3 = 64
⇒ a = 4
b = `144/"a" = 144/4 = 36`
Therefore, numbers are 4 and 36
APPEARS IN
RELATED QUESTIONS
If y is the mean proportional between x and z, prove that: `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`.
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
Determine if the following numbers are in proportion:
32, 48, 70, 210
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?
Which of the following ratios are in proportion?
10 g of caustic soda dissolved in 100 mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ______.
