12 : □ = □ : 4 = 8 : 16 - Mathematics

12 : `square` = `square` : 4 = 8 : 16

Fill in the Blanks

12 : 24 = 2 : 4 = 8 : 16

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Chapter 3: Ratio and Proportion - Exercise 3.3 [Page 58]

Chapter 3 Ratio and Proportion
Exercise 3.3 | Q 1. (iv) | Page 58

If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`

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

If p, q and r in continued proportion, then prove the following:

(p + q + r )(p - q + r) = p² + q² + r²

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

Find the mean proportion of: `(1)/(12) and (1)/(75)`

Verify the following:

39 : 65 : : 141 : 235

A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?

If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?

If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`

If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`