Learn on PengiEureka Math, Grade 4Chapter 9: Multiplicative Comparison Word Problems

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

In this Grade 4 Eureka Math lesson from Chapter 9, students solve multiplicative comparison word problems by applying the area formula (length × width) and the perimeter formula (2 × (length + width)) for rectangles and squares. Students use square-inch tiles and drawings to understand relationships such as "3 times as long as it is wide" and translate those comparisons into calculations. The lesson builds directly on students' prior knowledge of area and perimeter to connect multiplicative reasoning with real-world measurement contexts.

Section 1

Finding Area, Perimeter, and Unknown Side Lengths of a Rectangle

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

Section 2

Solving Multi-Step Comparison Problems with Area and Perimeter

Property

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

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

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Finding Area, Perimeter, and Unknown Side Lengths of a Rectangle

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

Section 2

Solving Multi-Step Comparison Problems with Area and Perimeter

Property

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

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

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Finding Area, Perimeter, and Unknown Side Lengths of a Rectangle

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

Section 2

Solving Multi-Step Comparison Problems with Area and Perimeter

Property

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

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