Question

pls give me the correct ans I will mark you as brainlist​

Answer 1

Solution:

Given That:

$\rm \longrightarrow a:b = 2:1$

$\rm \longrightarrow b:c = 3:1$

Can be written as:

$\rm \longrightarrow \dfrac{a}{b} = \dfrac{2}{1}$

$\rm \longrightarrow a = 2b - (i)$

And:

$\rm \longrightarrow \dfrac{b}{c} = \dfrac{3}{1}$

$\rm \longrightarrow b =3c - (ii)$

Now, the expression is:

$\rm = \bigg( \dfrac{ {a}^{2} }{6bc} \bigg)^{2}$

Can be written as:

$\rm = \bigg( \dfrac{ {(2b)}^{2} }{2b \times 3c} \bigg)^{2}$

$\rm = \bigg( \dfrac{2b}{3c} \bigg)^{2}$

Since b = 3c, we get:

$\rm = \bigg( \dfrac{2b}{b} \bigg)^{2}$

$\rm = {2}^{2}$

$\rm = 4$

★ Which is our required answer.

Answer:

$\rm \hookrightarrow \bigg( \dfrac{ {a}^{2} }{6bc} \bigg)^{2} = 4$

Learn More:

Two ratios a : b and c : d are proportional if,

→ Product of extremes = Product of means

→ a × d = b × c

And is written as:

→ a : b : : c : d

If a : b and c : d are two ratios such that a : b : : c : d. Then the following results hold true.

1. Invertendo.

$\rm\longrightarrow b : a : : d : c$

2. Alternendo.

$\rm\longrightarrow a : c : : b : d$

3. Componendo.

$\rm\longrightarrow (a + b) : b: : (c + d) : d$

4. Dividendo.

$\rm\longrightarrow (a - b) : b: : (c - d) : d$

5. Componendo and dividendo.

$\rm\longrightarrow (a + b) : (a - b): : (c + d) :(c - d)$

6. Convertendo.

$\rm\longrightarrow a : (a - b): :c:(c - d)$

Answer 2

Correct answer is 4…