Advertisements
Advertisements
Question
Find two numbers whose mean proportional is 18 and the third proportional is 486.
Advertisements
Solution
Let a and b be the two numbers, whose mean proportional is 18.
`therefore "ab" = 182 => "ab" = 324 => "b" = 324/"a"` ......(i)
Now, third proportional is 486
∴ a : b : : b : 486
⇒ b2 = 486 a
⇒ `(324/"a")^2` = 486 a
⇒ `(324)^2/"a"^2` = 486 a
⇒ `"a"^3 = (324 xx 324)/486`
⇒ a3 = 216
⇒ a = 6
b = `324/"a" = 324/6 = 54`
Therefore, numbers are 6 and 54 .
APPEARS IN
RELATED QUESTIONS
Find the fourth proportion to the following:
3,5 and 15
If x, 12 and 16 are in continued proportion! find x.
If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.
If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.
If 22.5 m of a uniform iron rod weighs 85.5 kg, what will be the weight of 5 m of the same rod?
If 12 L of diesel is consumed by a car in covering a distance of 222 km, how many kilometers will it go in 22 L of diesel?
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?
Determine if the following are in proportion.
24, 28, 36, 48
