If the area of a rectangle be (`x^(2) + 7x + 10)` sq. cm, then one of the possible perimeter of it is

Options

A. `(4x + 14) cm`
B. `(2x + 14) cm`
C. `(x + 14) cm`
D. `(2x + 7) cm`

Answer

To find the perimeter of the rectangle given its area, we can follow these steps:

### Step 1: Understand the Area of a Rectangle
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
In this case, the area is given as \(x^2 + 7x + 10\) square centimeters.

### Step 2: Factor the Area Expression
We need to factor the quadratic expression \(x^2 + 7x + 10\). We look for two numbers that multiply to 10 (the constant term) and add up to 7 (the coefficient of \(x\)).

The numbers 5 and 2 satisfy this condition:
\[ x^2 + 7x + 10 = (x + 5)(x + 2) \]

### Step 3: Assign Length and Breadth
From the factored form, we can assign:
- Length = \(x + 5\)
- Breadth = \(x + 2\)

### Step 4: Calculate the Perimeter
The perimeter \(P\) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the values of length and breadth:
\[ P = 2 \times ((x + 5) + (x + 2)) \]
Simplifying this:
\[ P = 2 \times (2x + 7) \]
\[ P = 4x + 14 \]

### Step 5: Conclusion
Thus, one possible perimeter of the rectangle is:
\[ \boxed{4x + 14} \]

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