Question

A general wishing to draw up his 16160 soldiers in the form of a solid square, found that he had 31 soldiers over. Find the number of men in the front line. ​

Answer 1

Answer:

127

Step-by-step explanation:

in a square all sides are equal, so there are same number of soldiers on all 4 sides

no. of soldiers= 16160

no of extra soldiers= 31

no. of soldiers in the form of square = 16160-31

                                                         = 16129

no . of soldiers in front line =√16129

= 127

Answer 2

$\bf{\huge{\underline{\boxed{\sf\purple{127\:men}}}}}$

$\rule{100}2$

$\textbf{\underline{\underline{Explanation:-}}}$

Given :

• Total soldiers = 16160
• Soldiers are to draw up in the form of a solid square
• He had 31 soldiers over.

To Find :

• The number of men in the front line.

→ Concept used :

• A  square has 4 equal sides. Hence, men drawn up in each side will be same.

$\sf\blue{\underline{\underline{Solution}}}$

Let side of the square be ' s ' unit.

Now,

According to Question :-

s² + 31 = 16160

⇒ s² = 16160 - 31

⇒ s² = 16129

⇒ ${s} =\sqrt{16129}$

∴ s = 167

Hence,

Answer : 127 men were drawn up in the front line.

$\rule{200}2$