Advertisements
Advertisements
Question
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Advertisements
Solution
Let x be the third proportional then
`a/b + b/c, sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab) : sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab sqrt(a^2 + b^2)) = sqrt(a^2 + b^2)/x`
⇒ x = `(ab (a^2 + b^2))/((a^2 + b^2))`
⇒ x = ab.
RELATED QUESTIONS
If `a/b = c/d` prove that each of the given ratios is equal to
`(5a + 4c)/(5b + 4d)`
Find the third proportion to the following :
3 and 15
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.
Determine if the following numbers are in proportion:
7, 42, 13, 78
Write (T) for true and (F) for false in case of the following:
51 : 68 : : 85 : 102
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?
The length and breadth of a school ground are 150 m and 90 m respectively, while the length and breadth of a mela ground are 210 m and 126 m, respectively. Are these measurements in proportion?
