Question

Pls answer this question ASAP.​

Answer 1

Answer:

3root29 option 1st is your answer

Answer 2

$\large\text{ \sqrt{ a^{2} +b^{2} +c^{2}}=87 }$

Let's set a parameter $k.$

Then, $k$ will satisfy the following equation.

$\cdots \longrightarrow 3a=4b=6c=k$

Now we have,

$\boxed{ \begin{aligned} &\rightarrow a=\dfrac{k}{3}\\\\&\rightarrow b=\dfrac{k}{4}\\\\&\rightarrow c=\dfrac{k}{6}. \end{aligned} }$

So,

$\cdots \longrightarrow \dfrac{ k }{ 3 } + \dfrac{ k }{ 4 } + \dfrac{ k }{ 6 } = 27 \sqrt{29}$

$\cdots \longrightarrow \dfrac{ 9k }{ 12 } = 27 \sqrt{29}$

$\cdots \longrightarrow \dfrac{ 3k }{ 4 } = 27 \sqrt{29}$

$\cdots \longrightarrow k= \dfrac{4}{3} \times 27 \sqrt{29}$

$\cdots \longrightarrow k= 36 \sqrt{29}.$

As we know,

$\boxed{ \begin{aligned} \sqrt{ a^{2} +b^{2} +c^{2} }&=\sqrt{ \left(\dfrac{k}{3} \right)^{2} +\left( \dfrac{k}{4}\right)^{2} +\left( \dfrac{k}{6}\right)^{2} }\\\\&= \sqrt{ \dfrac{1}{9} + \dfrac{1}{16} + \dfrac{1}{36} }|k|\\\\&= \sqrt{ \dfrac{16+9+4}{144} }|k|\\\\&= \sqrt{ \dfrac{29}{144} } |k|\\\\&= \dfrac{ \sqrt{ 29 } }{12}\times 36\sqrt{29}\\\\&=3 \times 29\\\\&=87. \end{aligned} }$

Hence, option (3) is correct.