Question

The length y of a rectangle is four less than three times the width x. The perimeter of the rectangle is 16 cm.

Answer 1

There is no requirement in the question. I'll calculate the area of the rectangle to help you with this question.

Answer:

`A=15\ cm^2`

Explanation:

System of Equations

Let's call y to the length of a rectangle, x to its width. There are two conditions that will help us to solve for x and y.

• The length is four less than three times the width. That is written as:

`y=3x-4`

• The perimeter of the rectangle is 16 cm. The equation for this condition is:

`2x+2y=16`

Divide by 2:

`x+y=8`

To solve the system, we'll substitute the y in the first equation into the second:

`x+3x-4=8`

Joining like terms:

`4x=8+4`

Solving:

`x=12/4=3`

Find the value of y:

`y=3x-4=3*3-4=9-4=5`

Thus, the length of the rectangle is 5 cm and its width is 3 cm. The area is calculated as:

`A=xy=3\ cm\cdot 5\ cm=15\ cm^2`

`\boxed{A=15\ cm^2}`