<u>Given</u>:
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.
<u>Equations of the two rectangles:</u>
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 ![a_2=3a_1-12](https://tex.z-dn.net/?f=a_2%3D3a_1-12)
<u>Areas of the two rectangles:</u>
The areas of the two rectangles can be determined using substitution method.
Thus, substituting
in the equation
, we get;
![a_1+3a_1-12=212](https://tex.z-dn.net/?f=a_1%2B3a_1-12%3D212)
![4a_1-12=212](https://tex.z-dn.net/?f=4a_1-12%3D212)
![4a_1=224](https://tex.z-dn.net/?f=4a_1%3D224)
![a_1=56](https://tex.z-dn.net/?f=a_1%3D56)
Thus, the area of the first rectangle is 56 m²
Substituting
in the equation
, we get;
![a_2=3(56)-12](https://tex.z-dn.net/?f=a_2%3D3%2856%29-12)
![a_2=168-12](https://tex.z-dn.net/?f=a_2%3D168-12)
![a_2=156](https://tex.z-dn.net/?f=a_2%3D156)
Thus, the area of the second rectangle is 156 m²
Hence, the area of the two rectangles are 56 m² and 156 m²