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
[tex]a_1+a_2=212[/tex] and [tex]a_2=3a_1-12[/tex]
Areas of the two rectangles:
The areas of the two rectangles can be determined using substitution method.
Thus, substituting [tex]a_2=3a_1-12[/tex] in the equation [tex]a_1+a_2=212[/tex], we get;
[tex]a_1+3a_1-12=212[/tex]
[tex]4a_1-12=212[/tex]
[tex]4a_1=224[/tex]
[tex]a_1=56[/tex]
Thus, the area of the first rectangle is 56 m²
Substituting [tex]a_1=56[/tex] in the equation [tex]a_2=3a_1-12[/tex], we get;
[tex]a_2=3(56)-12[/tex]
[tex]a_2=168-12[/tex]
[tex]a_2=156[/tex]
Thus, the area of the second rectangle is 156 m²
Hence, the area of the two rectangles are 56 m² and 156 m²
