Question

Mrs.Ali wants to buy a carpet for her square drawing room.If the carpet measures 324 square metres what is the length of each side of the drawing room​​

Answer 1

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Given:-

Mrs. Ali wants to buy a carpet for her square drawing room.

Carpet measures 324 m²

To Find:-

The length of each side of the drawing room.

Solution:-

Since the drawing room is square in shape, we need to keep the formula of finding the area of the square while trying to find the measure of the side of the square.

Area of Square → (Side)²

Area of Room = 324 m²  

Side = x

Using the formula, let's find the measure of the side of the drawing room.

(x)² = 324

Step 1: Find the square root of both sides of the equation.

⇒ √(x)² = √324

⇒ x = √324

To find the square root, we'll use the prime factorization method.

First, we'll prime factorize 324.

$\begin{gathered}\begin{array}{c|c} \tt 2 & \sf{ 324} \\ \cline{1-2} \tt 2 & \sf { 162} \\ \cline{1-2} \tt 3 & \sf{ 81} \\ \cline{1-2} \tt 3 & \sf{ 27} \\ \cline{1-2} \tt 3 & \sf{ 9 }\\ \cline{1-2} \tt & \sf{ 3}\\ \end{array}}\end{gathered}$

324 → 2 × 2 × 3 × 3 × 3 × 3

Now we'll pair the prime factors.  

324 → (2 × 2) × (3 × 3) × (3 × 3)

Finally, take one prime factor from each pair and multiply.

√324 → 2 × 3 × 3

√324 → 18

∴ x = 18

∴ The length of each side of the drawing room is 18 m

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Answer 2

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Given:-

Mrs. Ali wants to buy a carpet for her square drawing room.

Carpet measures 324 m²

__________________________

To Find:-

The length of each side of the drawing room.

__________________________

Solution

Since the drawing room is square in shape, we need to keep the formula of finding the area of the square while trying to find the measure of the side of the square.

Area of Square → (Side)²

Area of Room = 324 m²

Side = x

Using the formula, let's find the measure of the side of the drawing room.

(x)² = 324

Step 1: Find the square root of both sides of the equation.

⇒ √(x)² = √324

⇒ x = √324

To find the square root, we'll use the prime factorization method.

First, we'll prime factorize 324.

$\begin{gathered}\begin{array}{c|c} \tt 2 & \sf{ 324} \\ \cline{1-2} \tt 2 & \sf { 162} \\ \cline{1-2} \tt 3 & \sf{ 81} \\ \cline{1-2} \tt 3 & \sf{ 27} \\ \cline{1-2} \tt 3 & \sf{ 9 }\\ \cline{1-2} \tt & \sf{ 3}\\ \end{array}}\end{gathered}$

324 → 2 × 2 × 3 × 3 × 3 × 3

Now we'll pair the prime factors.

324 → (2 × 2) × (3 × 3) × (3 × 3)

Finally, take one prime factor from each pair and multiply.

√324 → 2 × 3 × 3

√324 → 18

∴ x = 18

∴ The length of each side of the drawing room is 18 m

__________________________