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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Narutoislifeviz Narutoislifeviz · Answer 1

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❌