Question

In an auditorium, the number of rows is equal to the number of chairs in each row. If the capacity of the auditorium is 3025, find the number of chairs in each row.

Answer 1

In Auditorium No of Rows is let be x
no. of rows and no. of chairs are same

So equations is
No. of chair × No.of rows =3025
x × x = 3025
${x}^{2} = 3025$
$x = \sqrt[2]{3025}$
$x = 55$
No of chair and Rows is 55

Answer 2

Answer:

The number of chairs in each row = 55

Step-by-step explanation:

Given,

The total seating capacity of the auditorium = 3025

The number of chairs in each row = The number of rows

To find,

The number of chairs in each row

Solution

Let the number of chairs in each row be 'x'

Since the number of chairs in each row = The number of rows, we have

The number of rows = x

We have,

The total capacity of the auditorium = The number of chairs in  a row × Total number rows

Substituting the values we get

3025 = x×x

3025 = x²

x = $\sqrt{3025}$

The prime factorization of 3025 is

3025 =  5x5x11x 11

=  5² x11²

$\sqrt{3025}$= $\sqrt{5^2X11^2}$

= 11x 5

= 55

x = $\sqrt{3025}$ = 55

∴The number of chairs in each row = 55

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