The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area (A) of the room?

Rationale

A = x(x + 5) is the correct equation representing the area of the room.

This equation accurately represents the formula for the area of a rectangle, which is length multiplied by width. In this case, the length of the room is 'x + 5' (5 feet greater than its width 'x'). Therefore, to find the area, 'x' (width) is multiplied by 'x + 5' (length).

A (A = x(x + 5)) YOUR ANSWER

This is indeed the correct equation. It properly represents the area of a rectangle by multiplying the width 'x' by the length 'x + 5'. Since the length is 5 feet greater than the width, this equation accurately models the relationship.

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

This equation represents the perimeter of a rectangle, not the area. The formula for the perimeter of a rectangle is 2(length) + 2(width). Here, it calculates the sum of twice the width and twice the length, which is not what the question asks for.

C (A = x(x + 5)) CORRECT

This is the correct equation as stated earlier. It accurately represents the area of a rectangle by multiplying the width 'x' by the length 'x + 5'.

D (A = 5x) YOUR ANSWER

This equation could be misinterpreted as the area of a rectangle if one assumes that the width is 'x' and the length is '5'. However, it does not take into account that the length is actually 5 feet greater than the width, as stated in the question.

Conclusion

The correct representation of the area of a rectangle with a length that is 5 feet greater than its width is A = x(x + 5). This equation correctly multiplies the width 'x' by the length 'x + 5'. The other options either represent the perimeter of a rectangle or do not accurately reflect the relationship between length and width as given in the question.

The length of a rectangular room is 5 feet greater than its width. Which of the following equations represents the area (A) of the room?

A = x(x + 5) is the correct equation representing the area of the room.

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