Answer:
Proved
Step-by-step explanation:
Given
[tex]p = 80[/tex] ---- perimeter
[tex]a \to area[/tex]
Required
[tex]x^2 + 40x + a = 0[/tex]
The perimeter is calculated as:
[tex]p = 2(x + y)[/tex]
Where
[tex]x,y \to[/tex] the rectangle dimension
So, we have:
[tex]2(x + y) = 80[/tex]
Divide by 2
[tex]x + y = 40[/tex]
Make y the subject
[tex]y = 40 - x[/tex]
The area of the rectangle is:
[tex]a = xy[/tex]
[tex]a = x * (40 -x)[/tex]
[tex]a = 40x -x^2[/tex]
Equate to 0:
[tex]x^2 - 40x + a = 0[/tex]
