Question 31

A = x(x + 5)

The equation that represents the area (A) of the rectangular room, where the length is 5 feet greater than its width, is A = x(x + 5). Here, x represents the width, and (x + 5) represents the length.

A) A = x(x + 5)

This option is identical to the correct answer. It accurately represents the formula for the area of a rectangle, where the width is x and the length is x + 5, reflecting the relationship given in the question.

B) A = 2x + 2(x + 5)

This option suggests a formula for the perimeter of the rectangle rather than the area. The terms represent the addition of the widths and lengths, but do not provide a product, which is essential for calculating area.

C) A = x(x + 5)

This option is exactly the same as the correct answer. It appropriately represents the area of the rectangle by multiplying the width (x) by the length (x + 5).

D) A = 5x

This option implies that the area is a simple product of 5 and the width. It does not account for the length being 5 feet greater than the width, thus failing to accurately represent the area of the rectangle.

Conclusion

The correct answer, A = x(x + 5), is definitively right as it directly corresponds to the dimensions provided in the question. The other options either misrepresent the area calculation or provide incorrect formulas, making them unsuitable for representing the area of the rectangular room.