Answer:
16 by 9 feet.
Step-by-step explanation:
We have 50 feet of fencing in total.
Therefore, the perimeter of our area is 50. Perimeter is given by:
[tex]P=2(\ell+w)[/tex]
Substituting 50 for P yields:
[tex]50=2(\ell+w)[/tex]
And dividing both sides by 2 yields:
[tex]\ell+w=25[/tex]
The area of a rectangular is given by:
[tex]A=\ell w[/tex]
Where [tex]\ell[/tex] is the length and [tex]w[/tex] is the width.
We want to enclose 144 feet squared. So, A=144:
[tex]144=\ell w[/tex]
By the perimeter equation, we can subtract a variable, say [tex]\ell[/tex] from both sides. Hence:
[tex]w=25-\ell[/tex]
Now, we can substitute this into our area equation. Therefore:
[tex]144=\ell(25-\ell)[/tex]
Distribute:
[tex]144=25\ell-\ell^2[/tex]
Subtract 144 from both sides:
[tex]-\ell^2+25\ell-144=0[/tex]
Divide everything by -1:
[tex]\ell^2-25\ell +144=0[/tex]
Factor:
[tex](\ell-9)(\ell-16)=0[/tex]
Zero Product Property:
[tex]\ell_1=9\text{ or } \ell_2=16[/tex]
Then it follows that:
[tex]w_1=25-(\ell_1)=25-9=16[/tex]
Or:
[tex]w_2=25-(\ell_2)=25-(16)=9[/tex]
Regardless, the dimensions of the rectangular area will be 16 by 9 feet.
Answer:
p = 2(l +w)
l= p÷2 -w = l= 25 -w
A= l x w =( 25 -W)W= 144
-w^2 +25w-144 =0
-w^2 +9w+16w- 144=0
(-w^2+9w) +(16w- 144) =0
-w(w - 9) + 16(w - 9) =0
(-w +16) = 0 or w - 9 =0
w = 9 or w = 16
so l = 25 - 9 = 16
or l = 25 - 16 = 9
therefore l = 16ft and w= 9ft
