Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas.

Property

For a rectangle with length $l$ and width $w$:

• Area is calculated by multiplying length and width: $A = l \times w$.
• Perimeter is twice the sum of the length and width: $P = 2 \times (l + w)$.
• If the area and one side are known, the unknown side can be found by division: $w = \frac{A}{l}$ or $l = \frac{A}{w}$.

Examples

Property

To solve for a final area ($A_{new}$) or perimeter ($P_{new}$) after a multiplicative comparison, follow these steps:

1. Find the unknown dimension of the original shape (e.g., $w_{original} = \frac{A_{original}}{l_{original}}$).
2. Calculate the new dimensions using the scaling factor (e.g., $l_{new} = k \times l_{original}$).
3. Calculate the final area or perimeter using the new dimensions (e.g., $A_{new} = l_{new} \times w_{new}$).

Examples