Advertisements
Advertisements
प्रश्न
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
Advertisements
उत्तर
Let the two numbers are a and b.
∵ 28 is the mean proportional
∵ a : 28 : : 28 : b
∴ ab = (28)2 = 784
⇒ a = `(784)/b` ...(i)
∵ 224 is the third proportional
∴ a : b : : b : 224
⇒ b2 = 224a ...(ii)
Substituting the value of a in (ii)
b2 = `24 xx (784)/b`
⇒ b3 = 224 x 784
⇒ b2 = 175616 = (56)3
∴ b = 56
Now substituting the value of b in (i)
a = `(784)/(56)` = 14
Hence numbers are 14, 56.
APPEARS IN
संबंधित प्रश्न
If q is the mean proportional between p and r, show that: pqr(p + q + r)3 = (pq + qr + rp)3.
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Given, `x/(b - c ) = y/(c - a ) = z/(a - b)` , Prove that
ax+ by + cz = 0
What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
Sleeping time of a python in a 24 hour clock is represented by the shaded portion in the following figure.
The ratio of sleeping time to awaking time is ______.
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?
