The area of a rectangular field is 2275 m2. The field is enclosed by 200 m of fence. What are the dimensions of the field?

So it is enclosed by 200 m of fence

perimiter=200 m

it is a rectangle to

p=legnth+legnth+width+width or

p=l+l+w+w or

p=2l+2w or

p=2 (l+w)

so

p=200

200=2 (l+w)

divide both sides by 2

100=l+w

area=l times w

area=2275

lw=2275

l+w=100

combine and solve

l+w=100

subtract w

l=100-w

subisutute 100-w for l in other eqution

(100-w) (w) = 2275

distribute

-w^2+100w=2275

add (w^2-100w) to both sides

0=w^2-100w+2275

factor

find what 2 numbers add up to - 100 and multiply to get 2275

guess (or factor 2275 and find factors that add up to - 100)

figure out that they are - 65 and - 35

0 = (w-65) (w-35)

set each to zero

0=w-65

0=w-35

solve for w

w=65 or 35

65>35 so

65 m=legnth

35 m=width