Determine the lengths of the sides of the rectangle using the given area. give answers both exactly and
approximately (to the nearest tenth).
the area of the rectangle is 70 cm-.
the width of the rectangle is
cm.
the length of the rectangle is.
cm.

Part a) Exactly values

The width of the rectangle is

The length of the rectangle is

Part b) Approximately values

The width of the rectangle is

The length of the rectangle is

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of rectangle is equal to

we have

substitute the values in the formula

so

Solve for x

Divide by 4 both sides

square root both sides

The solution is the positive value

therefore

Exactly values

Approximately values

1696 hundred thousand

step-by-step explanation:

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.