Question

Kathryn is making a flag for her school's football team. She has 40 feet of trim to put around the

edge of the flag. The graph shows the function for the width, w(x), the length, l(x), and the area,
A(x), of the flag. Write a function rule, A(x), for the area of the flag in terms of the given amount
of edging material
a. 30
b. 40
c. 40
d. 10
e. 60
f. 300
g. 20

Answer 1

To write a function rule for the area of the flag in terms of the given amount of edging material, we set up an equation using the perimeter of the flag. Solving the equation, we find the function rule to be A(x) = (40x - 2x^2)/2.

Step-by-step explanation:

In this problem, we are given 40 feet of trim to put around the edge of the flag. We are asked to write a function rule, A(x), for the area of the flag in terms of the given amount of edging material. Since the trim will go around the edge of the flag, it will contribute to both the length and the width of the flag.

Let's assume the width of the flag is w, and the length of the flag is l. We know that the perimeter of the flag, P, is equal to 2w + 2l (since there are two widths and two lengths). We are given that the perimeter is 40 feet, so we can set up the equation:

2w + 2l = 40

To get the function rule for the area, A(x), we need to express either w or l in terms of the other variable. Let's solve the equation for l:

2l = 40 - 2w

l = (40 - 2w)/2

The area of the flag, A, is equal to the product of the width and length:

A = w * l

Substituting the value of l, we get:

A = w * ((40 - 2w)/2)

Simplifying, we get:

A = (40w - 2w^2)/2

Therefore, the function rule for the area of the flag, A(x), in terms of the given amount of edging material is A(x) = (40x - 2x^2)/2.