The perimeter of a rectangle is forty inches. The length is two inches more than three times the width. Find the dimensions of
the rectangle.

Let Width (inches)  = X

Let Length (inches) = 3x + 2

40 = (x) + (3x + 2) + (x) + (3x +2)

40 = 8x + 4

-4           -4

36 = 8x

/8     /8

4.5 = x (width)

Length = 3x + 2

length = 3(4.5) + 2

length = 13.5 + 2

length = 15.5 inches

CHECK

40 = 15.5 + 4.5 + 15.5 + 4.5

40 = 20 + 20

40 = 40

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.