A rectangle has an area of `144 cm^(2)`. If the length is 7 cm more than the breadth of the rectangle. Find the sides of the rectangle.

Options

A. 12 cm
B. 9 cm
C. 16 cm
D. 15 cm

Answer

To find the sides of the rectangle, we will follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangle be \( B \) cm. According to the problem, the length \( L \) of the rectangle is 7 cm more than the breadth. Therefore, we can express the length as:
\[ L = B + 7 \]

### Step 2: Write the formula for the area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times B \]
We know from the problem that the area is \( 144 \, \text{cm}^2 \). Substituting the expression for length, we have:
\[ 144 = (B + 7) \times B \]

### Step 3: Set up the equation
Expanding the equation gives us:
\[ 144 = B^2 + 7B \]
Rearranging this equation to set it to zero, we get:
\[ B^2 + 7B - 144 = 0 \]

### Step 4: Factor the quadratic equation
Now, we need to factor the quadratic equation \( B^2 + 7B - 144 = 0 \). We look for two numbers that multiply to \(-144\) and add to \(7\). The numbers \(16\) and \(-9\) fit this requirement:
\[ (B + 16)(B - 9) = 0 \]

### Step 5: Solve for \( B \)
Setting each factor to zero gives us:
1. \( B + 16 = 0 \) → \( B = -16 \) (not valid since breadth cannot be negative)
2. \( B - 9 = 0 \) → \( B = 9 \)

Thus, the breadth of the rectangle is \( 9 \, \text{cm} \).

### Step 6: Calculate the length
Now, we can find the length using the expression we derived earlier:
\[ L = B + 7 = 9 + 7 = 16 \, \text{cm} \]

### Final Answer:
The sides of the rectangle are:
- Breadth = \( 9 \, \text{cm} \)
- Length = \( 16 \, \text{cm} \)

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