Question

A bulletin board has a perimeter of 200 inches. Which equation expresses the area A(w) of the bulletin board as a function of its width, w?
A. A(w) = 100w - w2
B. A(w) = 200w - w2
C. A(w) = w2 – 100w
D. A(w)=w2 - 200w​

Answer 1

Answer: A(W) = 100W -$W^{2}$

Step-by-step explanation:

The formula for calculating the perimeter is given as :

P = 2 ( L + W )

the perimeter is given as 200 , that is

200 = 2 ( L + W )

Dividing through by 2 , we have

100 = L + W

Make L the subject of the formula ;

L = 100 - W

The formula for the area is given as Length x width , substituting the values , we have :

A = LW , since , L = 100 - W , we have

A = (100- W) (W)

A = 100W -$W^{2}$

Therefore :

A(W) = 100W -$W^{2}$