Advertisements
Advertisements
Question
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
Advertisements
Solution
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
RELATED QUESTIONS
Find the third proportional to a – b and a2 – b2
Find the fourth proportion to the following:
0.7, 4.9 and 1.6
Find the fourth proportion to the following :
(x2 - y2),(x3 + y3)anc(x3 - xy2 + x2y- y3)
If a : b = c : d, show that (a - c) b2 : (b - d) cd = (a2 - b2 - ab) : (c2 - d2 - cd).
If `x/a = y/b = z/c`, prove that `[(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3 = "xyz"/"abc"`
Choose the correct answer from the given options :
The fourth proportional to 3, 4, 5 is
What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
If `(a + b)^3/(a - b)^3 = 64/27`
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.
