Answer:
Length = 14 in, width = 7 in
Step-by-step explanation:
The area of the page [tex]= l \times w = 98[/tex]
[tex]lw = 98[/tex]
The length of the printable area is gotten by subtracting the top and bottom margins from the length of the page [tex]= l - 1 - 1 = l - 2[/tex]
The width of the printable area is gotten by subtracting the left and right margins from the width of the page [tex]w - \frac{1}{2}- \frac{1}{2} = w-1[/tex]
The area of the printable area is
[tex]A = (l-2)(w-1) = lw - l - 2w + 2[/tex]
But [tex]lw = 98[/tex],
[tex]A = 98-l-2w+2 = 100-l-2w[/tex]
Also, from [tex]lw = 98[/tex],
[tex]l = \dfrac{98}{w}[/tex]
[tex]A = 100 - \dfrac{98}{w} - 2w[/tex]
To maximize this area,
[tex]\dfrac{dA}{dw} = 0[/tex]
[tex]\dfrac{98}{w^2} - 2 = 0[/tex]
[tex]\dfrac{98}{w^2} = 2[/tex]
[tex]2w^2 = 98[/tex]
[tex]w^2=49[/tex]
[tex]w=7[/tex]
Hence,
[tex]l = \dfrac{98}{7}=14[/tex]
