To find the perimeter of a rectangular house in terms of its area, we start with the given dimensions: the width \( w \) is 2 and the length \( l \) is \( a \).
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Calculate the area (b): The area \( b \) of the rectangle is given by the formula: \[ b = \text{width} \times \text{length} = 2 \times a = 2a \]
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Calculate the perimeter (P): The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) = 2 \times (a + 2) \] Simplifying this gives: \[ P = 2a + 4 \]
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Express the perimeter in terms of the area (b): From the area equation \( b = 2a \), we can express \( a \) in terms of \( b \): \[ a = \frac{b}{2} \] Substituting \( a \) back into the perimeter equation: \[ P = 2\left(\frac{b}{2}\right) + 4 = b + 4 \]
Thus, the perimeter \( P \) of the house can be expressed in terms of the area \( b \) as: \[ P = b + 4 \]