Question

A bulletin board has a perimeter of 200 inches. Which expression expresses the area A(w) of the bulletin board as a function of its width, w?

Answer 1

area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w-
`w^(2)`

Explanation:

• let, the shape of the bulletin board is a rectangle,

• then the perimeter of it = sum of all sides

= 2[length+width] = 2[l+w]

(let l: length, w : width )

• so, 200 = 2[l+w]

100= l+w ( dividing both the sides by 2)

so, l= 100-w

• area = length*width=l*w=[100-w]*w

• therefore,area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w-
  `w^(2)`