Advertisements
Advertisements
प्रश्न
Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.
Advertisements
उत्तर
Let a and b be the two numbers, whose mean proportional is 12.
∴ ab = 122
`=>` ab = 144
`=> b = 144/a` ...(i)
Now, third proportional is 96
∴ a : b :: b : 96
`=>` b2 = 96a
`=> (144/a)^2 = 96a`
`=> (144)^2/a^2 = 96a`
`=> a^3 = (144 xx 144)/96`
`=>` a3 = 216
`=>` a = 6
`b = 144/6 = 24`
Therefore, the numbers are 6 and 24.
संबंधित प्रश्न
Find the fourth proportional to 1.5, 4.5 and 3.5
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
If a, b, c are in continued proportion, prove that a : c = (a2 + b2) : (b2 + c2).
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
Determine if the following numbers are in proportion:
7, 42, 13, 78
Choose the correct statement:
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?
If two ratios are equal, then they are in ______.
The shadow of a 3 m long stick is 4 m long. At the same time of the day, if the shadow of a flagstaff is 24 m long, how tall is the flagstaff?
