Solving problem.
A square and a rectangle have the same area. The lengths of the side of the rectangle are integers and the perimeter is 28 cm. Which of the areas below cannot be the same area of the square? Justify your answer.
a. 40 m²
b. 42 m²
c. 45 m²
d. 33m²
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Answer:
B
Step-by-step explanation:
A. 40 m^2 = 4m x 10m
Perimeter = 2(4m) + 2(10m) = 8m + 20m = 28m✔️
C. 45 m^2 = 5m x 9m
Perimeter = 2(5m) + 2(9m) = 10m + 18m = 28m✔️
D. 33 m^2 = 3m x 11m
Perimeter = 2(3m) + 2(11m) = 6m + 22m = 28m✔️
Meanwhile, for B:
> If 42 m^2 = 6m x 7m
Perimeter = 2(6m) + 2(7m) = 12m + 14m = 26m❌
> If 42 m^2 = 2m x 21m
Perimeter = 2(2m) + 2(21m) = 4m + 42m = 46m❌
> If 42 m^2 = 3m x 14m
Perimeter = 2(3m) + 2(14m) = 6m + 28m = 34m❌