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
If a, b and c are in continued proportion, prove that `(a^2 + b^2 + c^2)/(a + b + c)^2 = (a - b + c)/(a + b + c)`
If a : b = c : d; then show that (ax+ by) : b = (cx+ dy) : d
Find the third proportional to `5(1)/(4) and 7.`
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?
If a, b, c and d are in proportion, prove that: `(a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"`
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
3 : 5 : : `square` : 20
Are the following statements true?
7.5 litres : 15 litres = 5 kg : 10 kg
