A banner has a red border and a rectangular white centre The

A banner has a red border and a rectangular white centre. The width of the border at and bottom is 8 inches. along the sides it is 6 inches. The total area of the banner is 27 square feet. What should be the dimensions of the banner if the area of the white centre is to be maximized.

Solution

To MAximise the Area of the White Board

Length = Width

So

Let the Dimmensions of the Banner be x and y

Therefore

x*y = 27 ------(1)

Also

(x-8)= (y-6) ----------(2)

So by Solving Eq(1) and (2) we get

x = 1 + 27

= 6.291 feet

y = - 1 + 27

= 4.291 feet