This is a word problem, that I need solved. I need t solved in the lowest terms.
Among all rectangles that have a perimeter of 60, find the dimensions of the one whose area is largest.
Here's an algebraic solution.
x = width of rectangle
y = length of rectangle
x + y = 30 ==> y = 30 – x
Area, A = xy = x(30–x)
A(x) is a quadratic that graphs as a parabola opening down (-x^2);
so Vertex will be maximum point on parabola.
Zeros of A(x): x = 0 and x = 30
Axis of Symmetry: x = 30/2 = 15.
So largest rectangle with perimeter of 60 has:
width = 15, and
length = 30 – 15 = 15.
It's a square.