Advertisements
Advertisements
Question
If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Advertisements
Solution
Let x, y and z are the three quantities which are in continued proportion
Then, x : y :: y : z => y2 = xz
Now, we have to prove that
x : z = x2 : y2
⇒ xy2 = x2z
LHS
= xy2 = x(xz) = x2z = RHS
LHS = RHS
APPEARS IN
RELATED QUESTIONS
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Find the fourth proportional to 3a, 6a2 and 2ab2
Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)
There is a number in the box `square` such that `square`, 24, 9, 12 are in proportion. The number in the box is ______.
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
