Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Check whether the following numbers are in continued proportion.
2, 4, 8
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
Determine if the following numbers are in proportion:
4, 6, 8, 12
If 57 : x : : 51 : 85, then the value of x is
The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?
Find the missing number in the box in the proportions:
`3/8 = square/20`
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.
