A seminar hall has 1764 seats in the form of rows, each rows containing as many seats as there are rows. How many seats are there in each row?

Given: 

Total number of seats  =  1764

A number of rows and number of seats in a row are equal.

To find: Total  number of seats in each row

Solution: So,  Lets take

Number of rows  = $x$

number of seats in a row  =  $x$

Number of rows  $\times$  number of seats in a row  =  Total number of seats

  $x\times x$     =  1764

  $x^{2}$     =   1764

To find the square root , find the factors of 1764

Factors of 1764   -   2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 7 $\times$ 7 

So ,       $x^{2}$    =   2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 7 $\times$ 7 

$x$=  √2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 7 $\times$ 7 

$x$=  2 $\times$ 3 $\times$ 7

$x$=  42

So , Number of rows  = 42

Number of seats in each row  =  42

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Updated on: 10-Oct-2022

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