Question

The perimeter of a college athletic field is 100 meters and the length is 18 m more than the width. How do you find the length and width. How would I find the answer?

Answer 1

Length = 34m
Width = 16m

Explanation:

I would form an algebraic expression from the information given:

Let length of field be represented by `x` and width by `y`.

We are told that perimeter is 100m, so `2x+2y=100`
which simplifies to:
1. `x+y=50`
by dividing both sides by 2

The other info tells us that length,`x` is 18m more than width,`y`:
2. `=>x=y+18`

Then solve the equations simultaneously (I have used substitution):
`(y+18)+y=50`
`=> 2y= 50-18`
`=>y=32/2`
`=>y=16`

Then substitute back into either equation to obtain `x`:
2. `x=16+18 = 34`

Double check by making sure `2x+2y=100`

Hope this helps!

Answer 2

`color(magenta)("The width of the field is 16 meters and the length is 34 meters"`

Explanation:

`"Given that:"`

`"Perimeter "` `=100` `" meters"`

`"Let us assume the width as "` `w` `" meters."`

`"So the length "` `=w+18` `" meters"`

`"According to question:"`

`"Perimeter"` `=2(l+w)`

`100=2(w+w+18)`

`100/2=w+w+18`

`50=2w+18`

`50-18=2w`

`32=2w`

`w=32/2`

`color(red)(w"=16 meters"`

`"So, we have found that the width is 16 meters."`

`"Length"=w"+18"`

`=16+18`

`color(red)("=34 meters"`

`color(magenta)("The width of the field is 16 meters and the length is 34 meters"`

`color(darkred)("As a check:-"`

Perimeter=`2(l+w)`

`100=2(34+16)`

`RHS= 2(34+16)`

`=2xx50`

`=100`

`LHS=100`

`"Since LHS = RHS",`

`"Hence it is proved that the length = 34 meters and the width = 16 meters."`

`"Hope this helps! :)"`