Question 124

A hall has a capacity of 2704 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row.

Open in App

Solution

Let the number of seats in each row be x.
Then, number of rows = Number of seats in each row = x
$∴$ Total seats $= x \times x = x^{2}$
According to the question,
$x^{2} = 2704$

$\begin{matrix} 52 5 & ¯ 27 ¯ 04 25 102 & 204 2040 \end{matrix}$

$\Rightarrow x = \sqrt{2704} = \sqrt{52 \times 52} ∴ x = 52$
Hence, there are 52 seats in each row.

Suggest Corrections

Similar questions

In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and number of seats in each row was reduced by 10, the total number of seats increased by 300. Find:

Q. There are 500 seats in Minerva Cinema, Mumbai, placed in similar rows. After the reconstruction of the hall, the total number of seats became 10% less. The number of rows was reduced by 5 but each row contained 5 seats more than before. How many rows and how many seats in a row were there initially in the hall?

In an auditorium. seats were arranged in rows and columus. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats increased by 300. Find :

(i) the number of rows in the original arrangement.

(ii) the number of seats in the auditorium after re-arrangement.

Q. The seats in an arena are arranged so that each row is longer than the row in front of it by the same number of seats. The 13th row has 71 seats and the 19th row has 95 seats. Determine the total number of seats in the front three rows combined.

Q. The front row of an auditorium has