The ratio between the length and breadth of a rectangle is 3:2. If the area of the rectangle is 96 cm², then the length of the rectangle is:

Question

Accepted Answer

#### Step 1: Represent Length and Breadth
Let the length and breadth of the rectangle be $$3x$$ and $$2x$$, respectively, based on the given ratio $$3:2$$.

#### Step 2: Use the Area Formula
The area of a rectangle is given by:  
$$
	ext{Area} = 	ext{Length} 	imes 	ext{Breadth}.
$$  
Substitute the values:  
$$
96 = (3x) 	imes (2x).
$$

#### Step 3: Solve for $$x$$
Simplify the equation:  
$$
96 = 6x^2.
$$  
Divide both sides by 6:  
$$
x^2 = \frac{96}{6} = 16.
$$  
Take the square root:  
$$
x = \sqrt{16} = 4.
$$

#### Step 4: Find the Length
The length is $$3x$$:  
$$
	ext{Length} = 3 	imes 4 = 12 \, 	ext{cm}.
$$

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Thus, the length of the rectangle is **12 cm**, making Option **(b)** correct.

Answer

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