# 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?

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 $2 x + 2 y = 100$
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. $\implies x = y + 18$

Then solve the equations simultaneously (I have used substitution):
$\left(y + 18\right) + y = 50$
$\implies 2 y = 50 - 18$
$\implies y = \frac{32}{2}$
$\implies y = 16$

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

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

Hope this helps!

Mar 26, 2018

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

#### Explanation:

$\text{Given that:}$

$\text{Perimeter }$$= 100$$\text{ meters}$

$\text{Let us assume the width as }$$w$$\text{ meters.}$

$\text{So the length }$$= w + 18$$\text{ meters}$

$\text{According to question:}$

$\text{Perimeter}$$= 2 \left(l + w\right)$

$100 = 2 \left(w + w + 18\right)$

$\frac{100}{2} = w + w + 18$

$50 = 2 w + 18$

$50 - 18 = 2 w$

$32 = 2 w$

$w = \frac{32}{2}$

color(red)(w"=16 meters"

$\text{So, we have found that the width is 16 meters.}$

$\text{Length"=w"+18}$

$= 16 + 18$

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=$2 \left(l + w\right)$

$100 = 2 \left(34 + 16\right)$

$R H S = 2 \left(34 + 16\right)$

$= 2 \times 50$

$= 100$

$L H S = 100$

$\text{Since LHS = RHS} ,$

$\text{Hence it is proved that the length = 34 meters and the width = 16 meters.}$

$\text{Hope this helps! :)}$