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 2025, find the number of chairs in each row.

• A. 40
• B. 35
• C. 45
• D. 90

Answer 1

The correct option is

C

45

Let the number of chairs in each row be x.

Then, the number of rows = x.

Total number of chairs in the auditorium
= $(x\times x)=x²$
But, the capacity of the auditorium = 2025 (given).
Therefore, $x^2=2025$
$2025=5\times 5\times 3\times 3\times 3\times 3=5^2\times 3^4$

$\Rightarrow \sqrt{\left(2025\right)}=\sqrt{(5^2\times 3^4)}=5\times 3\times 3=45$

$\therefore x=5\times 3\times 3=45$.