Answer:
Length=82
width= 46
Step-by-step explanation:
Given:
Area of Rectangle}= 3772
Perimeter of Rectangle=256
[tex]\textrm{Formula of Perimeter of rectangle} = 2(length+width)[/tex]
Substituting the values we get:
[tex]2(l+b)=256\\l+b=\frac{256}{2}\\l+b=128\\l=128-b[/tex]
Now
[tex]\textrm{Formula of Area of rectangle}= length\times width[/tex]
Substituting the values we get:
[tex]l \times b= 3772[/tex]
Now from above equation derived for length we will substitute value of l in the above equation we will get.
[tex]b(128-b)=3772\\128b-b^{2} =3772\\[/tex]
Now taking left hand side to right handside we get
[tex]b^{2} -128b+3772=0\\b^{2}-46b-82b+3772=0\\b(b-46)-82(b-46)=0\\(b-46)(b-82)=0\\[/tex]
Now solving for both equation we get.
[tex]b-46=0 \\ b=46[/tex]
[tex]b-82=0\\b=82[/tex]
from above we can conclude that
length=82
width=46
