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Word Problem 6 (Number of troops in a square)

Problem 6: A general wishing to draw up his 17429 men troops in the form of a solid square, found that he had 5 men over. The number of men in the front row is;

a. 132              b. 123                   c. 142                d. 152

Square area calculation

 

Solution:

 

Total number of troops = 17429

Men extra= 5

Men in front row=?

 

 

Here given that 5 men are over – i-e they are taken out to make a square.So,

Men In The Square=17429-5=17424

Because each side of square is equale in length, if 17424 troops stand in the form of a square, then each side of the square will have equal number of troops.

Let be ‘y’ be the length of each side of the square formed by standing troops. Then we know area of square can be calculated by taking square of one side, so the area of the square will be y² and that area is covered by the troops, so,

y ^{2}=17424

\Rightarrow y =\sqrt{17424}

\Rightarrow y =132

 

So, the number of troops in front or each row will be 132

 


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