Akiko wants to fence in her ft by ft vegetable garden. There will be a path ft wide between the garden and the fence. The area to be enclosed by the fence will be sq ft. Write a quadratic function that can be used to determine the value of .

see below

Step-by-step explanation:

The length is 12 + 2x  and the width is 10 + 2x

A = l*w

360 = ( 12+2x) ( 10+2x)

FOIL

360 = 120 + 24x+20x + 4x^2

Combine like terms

360 = 4x^2 +44x+120

Subtract 360 from each side

0 = 4x^2 +44x +120-360

0 = 4x^2+ 44x -240

For fun, lets solve

0 = 4( x^2 + 11x - 60)

0 = 4( x+15) ( x-4)

  Using the zero product property

x= -15  x=4

Since we cannot have negative length

x=4 ft

Step-by-step explanation:

Refer to the drawing.

We know that the area enclosed by the fence is 360 square feet. Remember that the area for a rectangle is given by the following formula:

So, let's substitute 360 for A, (12+2x) for b, and (10+2x) for h. This yields:

We can simplify this. On the right, factor out a 2 from the first term and a 2 from the second. This yields:

Multiply:

Divide both sides by 4:

Multiply on the right:

Add on the right:

Subtract 90 from both sides. So, our equation is:

And we're done!