If the area of a rectangle is 24 cm², what will be the area if each side is multiplied by 3?

If the area of a rectangle is 24 cm², what will be the area if each side is multiplied by 3?

• A. 72 cm²
• B. 216 cm²
• C. 48 cm²
• D. 96 cm²

Answer: (B)

To determine the area of the rectangle after each side is multiplied by 3, we start with the formula for the area of a rectangle, which is length multiplied by width. Given that the original area of the rectangle is 24 cm², if both the length and the width are multiplied by 3, the new dimensions become 3 times the length and 3 times the width. The new area can be calculated as: New Area = (3 × length) × (3 × width) = 9 × (length × width). Since the original area (length × width) is 24 cm², substituting that in gives us: New Area = 9 × 24 cm² = 216 cm². Therefore, when each side is multiplied by 3, the area increases by a factor of 9 (since 3 × 3 = 9), leading to the final area of 216 cm². This reflects how scaling each dimension of a shape impacts the overall area, specifically multiplying the area by the square of the factor by which the dimensions are scaled.

To determine the area of the rectangle after each side is multiplied by 3, we start with the formula for the area of a rectangle, which is length multiplied by width.

Given that the original area of the rectangle is 24 cm², if both the length and the width are multiplied by 3, the new dimensions become 3 times the length and 3 times the width. The new area can be calculated as:

New Area = (3 × length) × (3 × width) = 9 × (length × width).

Since the original area (length × width) is 24 cm², substituting that in gives us:

New Area = 9 × 24 cm² = 216 cm².

Therefore, when each side is multiplied by 3, the area increases by a factor of 9 (since 3 × 3 = 9), leading to the final area of 216 cm². This reflects how scaling each dimension of a shape impacts the overall area, specifically multiplying the area by the square of the factor by which the dimensions are scaled.