P = 2(l+w)
200 = 2(l+w)
divide by 2 on each side
100 = l+w
let the length = x
100 = x+w
solve for w but subtracting x from each side
100 -x = w
A= l*w
we know l =x
substitute for w because we found w above 100 -x = w
A = x * (100-x)
distribute
A = 100x - x^2
10. if A = 2400
2400 = 100x-x^2
subtract 100x from each side
2400 -100x = 100x-x^2 -100x
2400 -100x = -x^2
add x^2 to each side
2400-100x^2 + x^2 = -x^2 + x^2
x^2 -100x+2400 =0
factor
(x-60) (x-40) = 0
using the zero product property
x-60 = 0 x-40 = 0
x=60 x=40
If x=60 then 100 -x = w 100-60 = w w=40
If x=40 then 100 -x = w 100-40 = w w=60
The dimensions are 60m by 40 m