Answer:
[tex]l =45[/tex] --- length
[tex]w = 55[/tex] --- width
Step-by-step explanation:
Given
[tex]P = 200[/tex] --- perimeter
[tex]A = 2475[/tex] --- area
Required
The dimension of the farm
Let
[tex]l \to length; w \to width[/tex]
So:
[tex]p = 2(l+w)[/tex] --- perimeter
[tex]2(l+w)=200[/tex]
Divide by 2
[tex]l+w=100[/tex]
Make l the subject
[tex]l = 100 - w[/tex]
Also:
[tex]A= l*w[/tex] --- area
[tex]l * w = 2475[/tex]
Substitute: [tex]l = 100 - w[/tex]
[tex](100 - w) * w = 2475[/tex]
Open bracket
[tex]100w - w^2 = 2475[/tex]
Rewrite as:
[tex]w^2 - 100w +2475 = 0[/tex]
[tex]w^2 - 45w - 55w +2475 = 0[/tex]
Factorize
[tex]w(w - 45) - 55(w -45) = 0[/tex]
Factor out w - 45
[tex](w - 55)(w -45) = 0[/tex]
Take any one of the expression and solve for w
[tex]w -55 = 0[/tex]
[tex]w = 55[/tex]
Recall that: [tex]l = 100 - w[/tex]
[tex]l =100 - 55[/tex]
[tex]l =45[/tex]
