question on Quadratics (sidewalk around garden)

[cole92]

Well, I thought I was gonna breeze through this and the homework was mostly easy, but then I got to this problem and totally blanked:

Mrs. Mora wants to put a sidewalk around a rectangular garden. The garden is 14 feet wide and 36 feet long. The sidewalk will be the same width all the way around the garden.

The area of the sidewalk will be 300 feet. What will the be the sidewalk's width, x?

Here is what I have done so far but I get the feeling I am going about it all wrong:

(2x + 14) * (2x + 36)
4x[sup:2k9tipnk]2[/sup:2k9tipnk] + 72x + 28x + 504
4x[sup:2k9tipnk]2[/sup:2k9tipnk] + 100x + 504
4(x[sup:2k9tipnk]2[/sup:2k9tipnk] + 25x + 126)

From here I'm not exactly sure what to do. Complete the square? Or am I supposed to do something else? Any help would be appreciated. Look forward to any help and Thank You in advance

 

[galactus]

Re: question on Quadratics

You're almost there.

The area of the walk is 300 square feet.

So, we have \(\displaystyle (2x+14)(2x+36)-(36*14)=300\)

\(\displaystyle 4x^{2}+100x-300=0\)

You can complete the square, quadratic formula, whatever. It doesn't factor nicely so I would use the formula or complete the square.

 

[cole92]

Re: question on Quadratics

I'm confused as to where the minus 36 * 14 comes from.

Sorry if that isn't a good question :\ but from some reason it loses me

 

[galactus]

Re: question on Quadratics

The area of the whole kit and kaboodle is (2x+14)(2x+36). Right?. But the area of the walkway is 300. Therefore, we must subtract off the area of the pool which is 36*14=504.

 

[cole92]

Re: question on Quadratics

Ahhh, I looked at it completely wrong haha, I'm sorry.
Yes, I completely follow now, I'll just use the Quadratic formula to finish it off.

Thank you very much. I really appreciate the help!!!