Answer the question in the description

Question

A farmer has 1070 meters of fencing available to enclose a rentangular portion of his land 

(by the way theres a rentangle  the problem and on top of the rentangle it says x and on the right side of the rentangle it's y)

a.) write an equation to find the perimeter 

b.) find the expression for the height of the rentangle 

c.) express the area A of the rectangle as a function of x 

d.)for what value of x is the area largest 

e.) what is the largest area possible 

Answer 1

a)

 

The perimeter of rectangle is 2 the sum of the length and width.  So your perimeter equation will be

 

2(x + y) = 1070

 

x + y = 535

 

 

b)

 

The height is represented by y.  If we manipulate the perimeter equation to solve for y.

 

y = 535 - x

 

 

c)

 

The area of a rectangle is length times height.  So to form your equation for area use the previous answers to get the equation.

 

Area = xy

 

Area = x(535 - x)

 

 

Then just distribute.  You will end up with a quadratic function.

 

 

d)

 

Find the x-coordinate of the vertex.

 

 

e)

 

Evaluate the area at the x-coordinate of the vertex.