Question

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?​

Answer 1

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

`a_1+a_2=212` and
`a_2=3a_1-12`

Areas of the two rectangles:

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

Thus, substituting
`a_2=3a_1-12` in the equation
`a_1+a_2=212`, we get;

`a_1+3a_1-12=212`

`4a_1-12=212`

`4a_1=224`

`a_1=56`

Thus, the area of the first rectangle is 56 m²

Substituting
`a_1=56` in the equation
`a_2=3a_1-12`, we get;

`a_2=3(56)-12`

`a_2=168-12`

`a_2=156`

Thus, the area of the second rectangle is 156 m²

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