Find the Fourth Proportional To: 2xy, X2, Y2 - Mathematics

Find the fourth proportional to:
2xy, x², y²

Sum

Let A be the fourth proportional then
2xy : x² = y²: A
⇒ `(2xy)/x^2 = y^2/"A"`
⇒ A = `(x^2y^2)/(2xy)`
⇒ A = `(xy)/(2)`.

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Chapter 8: Ratio and Proportion - Exercise 1

Chapter 8 Ratio and Proportion
Exercise 1 | Q 17.1

Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.

Find the value of the unknown in the following proportion :

3 : 4 : : p : 12

If a, b, c and dare in continued proportion, then prove that

ad (c² + d²) = c³ (b + d)

Write (T) for true and (F) for false in case of the following:

45 km : 60 km : : 12 h : 15 h

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?

Choose the correct statement:

If `a/c = c/d = c/f` prove that : (b² + d² + f²) (a² + c² + e²) = (ab + cd + ef)²

If a, b, c are in continued proportion, prove that: a² b² c² (a^-4 + b^-4 + c^-4) = b^-2(a⁴ + b⁴ + c⁴)

If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)

5 : `square` : : 10 : 8 : : 15 : `square`