Advertisements
Advertisements
Question
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
Advertisements
Solution
Let the required third proportional be p.
`=> x/y + y/x, sqrt(x^2 + y^2)`, p are in continued proportion
`=> x/y + y/x : sqrt(x^2 + y^2) = sqrt(x^2 + y^2) : p`
`=> p(x/y + y/x) = (sqrt(x^2 + y^2))^2`
`=> p((x^2 + y^2)/(xy)) = x^2 + y^2`
`=>` p = xy
RELATED QUESTIONS
If `a/b = c/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
The sides of a triangle are in the ratio 1 : 3 : 5 and its perimeter is 90 cm. The length of its largest side is
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed
If 7 : 5 is in proportion to x : 25, then ‘x’ is
Are the following statements true?
45 km : 60 km = 12 hours : 15 hours
In the proportional statement p : q :: r : s, which pair of terms represents the means, and which pair represents the extremes?
