The area of a rectangular athletic field is represented by the expression 49x^2-9z^2 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.

Question

The area of a rectangular athletic field is represented by the expression 49x^2-9z^2  square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.

directrix · Answer

Do you know how to factor the difference of two squares, say a^2 - b^2?

directrix · Answer

Becasue that is all you need to do to 49x^2-9z^2 to get the answer.

anonymous · Answer

I could not find a common number in the two squares

directrix · Answer

There's not one. 
Look at it as (7x)^2 - (3z)^2 and factor that as the difference of two squares.

directrix · Answer

That's why I asked about factoring a^2 - b^2 to see if we needed to start there.

anonymous · Answer

o ok yea I remember reading that last night I must have for gotten. so basically the answer to this would be (7x)^2-(3z)^2 then how do I figure out the length and the width of the court to make the equation. i'm sorry i am really trying to get this it is alot to take in at one time

directrix · Answer

My computer will barely move on this site. I have to write on Word or Wordpad and copy my text here. Do you have that problem?

directrix · Answer

Let's factor. Yes, it is a lot to remember but we can still do it.

anonymous · Answer

no I don't have that problem at all

directrix · Answer

Your browser is ?

directrix · Answer

(7x)^2-(3z)^2 = ( 7x - 3z ) ( 7x + 3z )  following the a^2 - b^2 pattern of (a-b)(a+b)

anonymous · Answer

google chrome

anonymous · Answer

so basicaly after I factor the squares I creat the problem which is (7x-3z) is the length and (7x+3z) is the width therefore my solution to this would be (7x-3z)(7x+3z) square meters is this correct?

directrix · Answer

That is my understanding of the problem. Add the units which would be meters.

directrix · Answer

The question does say *an* acceptable set of dimensions which caused me to wonder if you were to make up a value of x and z but I don't think that is the case. I would go with the dimensions (7x-3z) meters  and (7x + 3z) meters.

anonymous · Answer

ok thank u so much

directrix · Answer

Do you have both Google Chrome and Internet Explorer on your computer or just the one.

Glad to help.

anonymous · Answer

I have both