Question

33. If 4, 10 and x are in continued proportion, what is the value of √x?​

Answer 1

Answer:

if a:b::c:d then bc=ad

so 4:10::10:x

x=25

Answer 2

$\\ \sf \large \underbrace{\: Understanding \: concept :- }$

Suppose : a , b and c are in continued proportion then a : b : c , So a × b = b × c Therefore, b² = ac

Now, Let's start

$\\ \sf \large \underline{\underline{ \: Given :-} }$

4 , 10 and x are in continued proportion.

$\\ \sf \large \underline{\underline{ \: Solution :-} }$

Let , 4 , 10 and x be a , b and c respectively.

So, we know that ,

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: {b}^{2} = ac$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: {10}^{2} = 4 \times x$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 100 = 4 x$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: x = \dfrac{100 }{4}$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: x = 25$

Now, We have to find $\sf \sqrt{x}$

$\\ \: \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \sqrt{x} = 5$

By taking square root on both side !

Hope it's helpful :)