Homework Sourse1 What is the largest rectangular area one can enclose with
1). What is the largest rectangular area one can enclose with 22 inches of string?
2). Solve the following quadratic equation for the indicated variable. (Enter your answers as a comma-separated list.)
x2 mx = 5 for x
3). Consider the following quadratic function.
f(x) = 3x2 12x + 8
Convert the function into standard form.
Solution
let length of rectangle = x
width of rectangle = y
given length of string = 22 inches
==> perimeter of rectangle = 22
==> 2(x + y) = 22
==> x + y = 22/2
==> x + y = 11
==> y = 11 - x
Now Area A = xy
==> A(x) = x(11 -x) = 11x - x2
Area is maximum ==> A \'(x) = 0
==> 11 - 2x = 0
==> 2x = 11
==> x = 11/2
==> y = 11 - 11/2 = 11/2
Hence maximum area = xy = (11/2)(11/2) = 121/4
==> maximum area = 30.25 square units
