Respuesta :
Answer:
length x is 50 feet
width y is 100 feet
Explanation:
three stalls of equal area
total built wall = 400 feet
to find out
what total length and width
solution
we consider here x and y is the length and width and area is rectangular
so
total linear feet will be
4 x + 2 y = 400
y = 200 - 2x
and
area = x y
area = x (200 -2x)
area = 200 x - 2x²
we know area maximum will be when x = [tex]\frac{-b}{2a}[/tex]
here a - 2 and b is 200
so
length x = [tex]\frac{-200}{2(-2)}[/tex] = 50 feet
width y = 200 - 2(-2) = 100 feet
The total length and width will give her the most floor space will be 50 feet and 100 feet respectively.
What is area of rectangle?
The number of unit squares that can fit into a rectangle is called its area. The flat surfaces of laptop displays, blackboards, painting canvas, and other rectangular forms are examples.
The area of a rectangle formula may be used to calculate the space occupied by these items.
Let the length be x and the width be y.
According to the condition the linear equation formed will be;
4 x + 2 y = 400
y = 200 - 2x
The area for a rectangle is given as the product of the length and breadth.
area = x y
area = x (200 -2x)
area = 200 x - 2x²
The value of maxima is obtained by differentiating the equation and equating it to zero.
The value of the area is maximum at
Here a value is 2 and b is 200
so[tex]\rm x= - \frac{b}{2a}[/tex]
If the value of a is 2 and b is 200;
The value of the length is found by;
[tex]\rm x= - \frac{200}{2\times(-2) } \\\\ \rm x= 50 feet[/tex]
length x = 50 feet
The width is found with the help of the length as y = 200 - 2x.Which is found as;
y = 200 - 2(-2) = 100 feet
Hence the total length and width will give her the most floor space will be 50 feet and 100 feet respectively.
To learn more about the area of the rectangle refer to the link;
https://brainly.com/question/14383947
