Question

Katie’s old bedroom was shaped like a rectangle. It had a length that was 3 times its width. When Katie’s family’s moved, her new bedroom was also shaped like a rectangle. It was 4 feet longer and 3 feet wider than old bedroom. If w represents the width of Katie’s old bedroom, which expression represents the difference between the area of her new bedroom and the area of her old bedroom

Answer 1

The expression for the difference between the areas of Katie's new and old bedrooms is obtained by subtracting the area of the old bedroom (3w^2) from the area of the new bedroom ((w + 3)(3w + 4)).

Step-by-step explanation:

Understanding the Area Difference

The question asks us to find the expression representing the difference between the areas of Katie's new bedroom and her old bedroom. In Katie's old bedroom, if w represents the width, then the length is 3w since it's stated that the length is three times the width. Therefore, the area of the old bedroom is w × 3w = 3w^2.

For Katie's new bedroom, which is 4 feet longer and 3 feet wider than her old bedroom, the dimensions would be (w + 3) for the width and (3w + 4) for the length. Thus, the area of her new bedroom is (w + 3)(3w + 4).

To find the difference in area, we subtract the old area from the new area: (w + 3)(3w + 4) - 3w^2. This expression would give us the change in the area when simplified.