Answer:
[tex]x^2+11x-60=0[/tex]
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:
[tex]A=bh[/tex]
So, let's substitute 360 for A, (12+2x) for b, and (10+2x) for h. This yields:
[tex]360=(12+2x)(10+2x)[/tex]
We can simplify this. On the right, factor out a 2 from the first term and a 2 from the second. This yields:
[tex]360=2(6+x)\cdot2(5+x)[/tex]
Multiply:
[tex]360=4(x+6)(x+5)[/tex]
Divide both sides by 4:
[tex]90=(x+6)(x+5)[/tex]
Multiply on the right:
[tex]90=x^2+6x+5x+30[/tex]
Add on the right:
[tex]90=x^2+11x+30[/tex]
Subtract 90 from both sides. So, our equation is:
[tex]x^2+11x-60=0[/tex]
And we're done!
