SOLUTION: Let the width(w) and the area(A) be real numbers. The perimeter remains a constant 24cm. Draw a graph for 1<=w<=11 that represents the relationship between the width and the area.

Question 1200298: Let the width(w) and the area(A) be real numbers. The perimeter remains a constant 24cm. Draw a graph for 1<=w<=11 that represents the relationship between the width and the area. Label the axes appropriately
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

x = width
P = perimeter
P = 2*length + 2*width
24 = 2*length + 2*width
12 = length + width
12 = length + x
length = 12-x

A(x) = area
A(x) = length*width
A(x) = (12-x)*x
A(x) = -x^2+12x

Graph of A(x) when 1 <= x <= 11

x = width
A(x) = area of the rectangle

Table of selected values

x	A(x)
1	11
2	20
3	27
4	32
5	35
6	36
7	35
8	32
9	27
10	20
11	11

(6,36) is the vertex since it's the highest point.
This vertex point tells us that the area is maxed out at 36 square cm when the width is x = 6 cm.

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