Algebra question

Question

I want to construct a fence around the perimeter of a field. The area of the field is 600 ft sq and the length of the field is 10 feet longer than the width.how many feet of fence will I need to fence in the field

Answer 1

L = length

W = width

A = Area

 

A = LxW

 

There are two equations:

 

LxW = 600

L = W + 10

 

Plug the right side of the second equation (W+10) into L in the first equation:

 

(W+10)(W) = 600

W² + 10W - 600 = 0

 

Factor or use the Quadratic Formula to solve for W:

 

W = 20

 

Plug W=20 back into either of the original equations to solve for L:

 

L = W + 10 = 20 + 10 = 30

 

W = 20

L = 30

Perimeter = 2L + 2W = (2)(30) + (2)(20) = 100

Answer 2

Let width = x

Let length = x + 10

 

Applying the area formula,

 

x(x + 10) = 600

 

 

Distribute the x.

 

x² + 10x = 600

 

 

Subtract 600 to both sides of the equation.

 

x² + 10x - 600 = 0

 

 

You can solve the quadratic equation for x from there.

 

Finally, apply the perimeter formula to find the number of feet of fencing needed.

 

Perimeter = 2(x + x + 10)

               = 2(2x + 10)

              = 4x + 20