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?

2 Answers
Mar 26, 2018

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!

Mar 26, 2018

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! :)"