The sum of the areas of two rectangles is 212 m². The second rectangle is 12 m² smaller than three times the first rectangle. What are the areas of the rectangles?

Given:

Given that the sum of the areas of two rectangles is 212 m². The second rectangle is 12 m² smaller than three times the first rectangle.

We need to determine the areas of the two rectangles.

Equations of the two rectangles:

Let a₁ denote the area of the first rectangle.

Let a₂ denote the area of the second rectangle.

The equations of the two rectangles is given by

 and  

Areas of the two rectangles:

The areas of the two rectangles can be determined using substitution method.

Thus, substituting in the equation , we get;

Thus, the area of the first rectangle is 56 m²

Substituting in the equation , we get;

Thus, the area of the second rectangle is 156 m²

Hence, the area of the two rectangles are 56 m² and 156 m²

the correct answer is 5 6 and 7