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:
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
Find the mean proportional to (x – y) and (x3 – x2y).
If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find the third proportional to 5, 10
Find the third proportional to 0.24, 0.6
If 15 tins of the same size contain 234 kg of oil, how much oil will there be in 10 such tins?
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If x, y, z are in continued proportion, prove that: `(x + y)^2/(y + z)^2 = x/z`.
