Question

The length of the rectangle garden is three feet less than twice its width. If the perimeter of the garden is 42 feet, what is its length? And please use the elimination method to solve this.

Answer 1

Data:

• Length ( ,l ,): three feet less than twice its width ( ,w ,).

,

• Perimeter ( ,P, ) = 42ft

Procedure

To solve this exercise, we have to build two equations based on the information given, as we have two variables.

• Length (l)

`l=2w-3`

where l and w represent the length and the width, respectively.

• Perimeter

`2l+2w=42`

To solve this system of equations, we can replace the expression of l in the second equation as follows:

`2\cdot(2w-3)+2w=42`

Simplifying:

`4w-6+2w=42`
`6w=42+6`
`w=(48)/(6)`
`w=8`

Now that we have the value of w, we can substitute in the first equation to get the value of l:

`l=2\cdot8-3`
`l=16-3`
`l=13`

Answer:

• Length 13 ft