Question

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?​​

Answer 1

Answer:

here is your answer, just do the mentioned

Answer 2

Given

• Seminar Hall has 1764 seats.
• The seats are in the form of rows.
• Each row contains as many seats as there are rows.

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To Find

• The number of seats in each row.

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Solution

Let's consider the number of seats in each row as ⇒ x

Total Number of seats in the Seminar Hall ⇒ x²

Number of seats in total ⇒ 1764

Now we have to solve this equation to obtain the answer ⇒ x² = 1764

Let's solve your equation step-by-step.

⇒ x² = 1764

Step 1: Simplify the equation.

⇒ x² = 1764

⇒ x = √1764

Step 2: Prime factorize 1764.

⇒ $\begin{array}{r | l} 2 & 1764 \\ \cline{2-2} 2& 882 \\ \cline{2-2} 3 & 441\\ \cline{2-2} 3 & 147 \\ \cline{2-2} 7 & 49\\ \cline{2-2} & 7 \\ \end{array}$

⇒ 1764 = 2 × 2 × 3 × 3 × 7 × 7

Step 2: Pair the product of primes.

⇒ 1764 = 2 × 2 × 3 × 3 × 7 × 7

⇒ 1764 = (2 × 2) × (3 × 3) × (7 × 7)

Step 3: Take one prime from each pair and multiply to obtain a perfect square.

⇒ √1764 = 2 × 3 × 7

⇒ √1764 = 42

∴ The number of seats in each row is 42.

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