Question

area = 20 m²
perimeter = 18 m
area = 20 m²
perimeter = 24 m

Explanation:

Step1: Determine the side length of the grid

Assume the grid is made of unit squares, so the side length of each small square is \( 1 \, \text{m} \) (since the unit is meters and the grid is for measuring length/area).

Step2: Find possible rectangles with area \( 20 \, \text{m}^2 \)

The area of a rectangle is \( A = l \times w \), where \( l \) is length and \( w \) is width. We need \( l \times w = 20 \). The factor pairs of 20 are: \( (1, 20) \), \( (2, 10) \), \( (4, 5) \).

Step3: Calculate perimeters for each factor pair

• For \( l = 4 \, \text{m} \), \( w = 5 \, \text{m} \): Perimeter \( P = 2(l + w) = 2(4 + 5) = 18 \, \text{m} \) (matches the first perimeter).
• For \( l = 2 \, \text{m} \), \( w = 10 \, \text{m} \): Perimeter \( P = 2(2 + 10) = 24 \, \text{m} \) (matches the second perimeter).
• For \( l = 1 \, \text{m} \), \( w = 20 \, \text{m} \): Perimeter \( P = 2(1 + 20) = 42 \, \text{m} \) (not matching either given perimeter, so we ignore this pair).

Answer:

The two rectangles with area \( 20 \, \text{m}^2 \) have dimensions \( 4 \, \text{m} \times 5 \, \text{m} \) (perimeter \( 18 \, \text{m} \)) and \( 2 \, \text{m} \times 10 \, \text{m} \) (perimeter \( 24 \, \text{m} \)).