Math
posted by Kim on .
you use a rectangular piece of cardboard 20 in by 30 to construct a box. you square the sides x in. from each corner of the piece of cardboard and then fold up the sides to form the bottom.
A. write a function A to represent the area of the base of the box in terms of x.
B. What is a reasonable domain for the function A?
C. Write an equation if the area of the base must be 416in^2
D. Solve the equation in part C for the values of x in the reasonable domain
What are the dimensions of the base of the box.

length of base = 302x
width = 202x
Area of base = (302x)(202x)
clearly 20x and 302x have to be positve, or
0 < x < 10
(302x)(202x) = 416
600  100x + 2x^2 = 416
2x^2  100x + 184
x^2  50x + 92 = 0
I will complete the square
x^2  50x + 625 = 92 + 625
(x25)^2 = 533
x25 = ± √533
x = 25 ± √533
so staying within the domain x = 25+√533
or appr. 1.91 
7+7