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 xx and width by yy.

We are told that perimeter is 100m, so 2x+2y=1002x+2y=100
which simplifies to:
1. x+y=50x+y=50
by dividing both sides by 2

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

Then solve the equations simultaneously (I have used substitution):
(y+18)+y=50(y+18)+y=50
=> 2y= 50-182y=5018
=>y=32/2y=322
=>y=16y=16

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

Double check by making sure 2x+2y=1002x+2y=100

Hope this helps!

Mar 26, 2018

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

Explanation:

"Given that:"Given that:

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

"Let us assume the width as "Let us assume the width as ww" meters." meters.

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

"According to question:"According to question:

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

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

100/2=w+w+181002=w+w+18

50=2w+1850=2w+18

50-18=2w5018=2w

32=2w32=2w

w=32/2w=322

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

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

"Length"=w"+18"Length=w+18

=16+18=16+18

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

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

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

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

100=2(34+16)100=2(34+16)

RHS= 2(34+16)RHS=2(34+16)

=2xx50=2×50

=100=100

LHS=100LHS=100

"Since LHS = RHS", since LHS = RHS,

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

"Hope this helps! :)"Hope this helps! :)