Among all rectangles that have a perimeter of 134, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.

The answer to this question would be: L= 33.5, W=33.5

In this question, the rectangle has a perimeter of 134. From this number, you can get this equation:

perimeter=134
2(L+W)= 134
L+W=67
L= 67-W

Using the formula for dimension you can get this equation:
dimension= L * W
dimension= (67-W)W= 67W- W^2

The maximum dimension should be differentiation of the equation which will look like:
67 -2w= 0
2w= 67
w= 33.5

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.