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
if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2 + 11n^2)`
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
Find the fourth proportional to:
x3 - y2, x4 + x2y2 + y4, x - y.
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
Choose the correct answer from the given options :
The fourth proportional to 3, 4, 5 is
Find two numbers whose mean proportional is 16 and the third proportional is 128.
If b : a = c : d, then a, b, c, d are in proportion.
Determine if the following are in proportion.
33, 121, 9, 96
Determine if the following are in proportion.
4, 6, 8, 12
