Mathematics: The length and width of a rectangle must add up to 78 feet. calculate the dimensions that will yield the maximum area (remember, area = length times width). what is the length that results in the maximum area?

can t understand questionStep-by-step explanation:...

The length and width of a rectangle must add up to

KenzieD6032

12.03.2022

The length that results in the maximum area is 39 feet.

Explanation

Lets assume, length of the rectangle is feet and width of the rectangle is feet.

As the length and width must add up to 78 feet, so the equation will be...

x+y=78 ................................................(1)

Solving equation (1) for y : y= 78-x

Now the area of the rectangle,

$A = x*y\\\\ A= x(78-x)\\\\ A= 78x-x^2\\\\ A= -x^2 +78x...................(2)$

will be maximum when $\frac{dA}{dx} = 0$

Now taking derivative of equation(2) with respect to ......

$\frac{dA}{dx}= -2x+78$

If $\frac{dA}{dx} =0$ , then

$-2x+78=0\\\\ -2x=-78\\\\ x=\frac{-78}{-2}=39$

If x= 39 , then y= 78-x = 78-39=39

So, both length and width will be 39 feet for getting maximum area.

The length that results in the maximum area is 39 feet.

0,0(0 оценок)