Area of Goalbox vs. Area of Penalty Box (rationals)

[mike_302]

Homework Statement

Area of goal box (soccer field) is described with (10x^2) / 27 and area of penalty box is described with (22x^2) / 9 . Determine how many times greater in size the penalty box is compared to the goal box.

Homework Equations

The Attempt at a Solution

I created the areas of the boxes based from dimensions, and simplified to what I have given (assume they are correct). Just don't get how to figure out that size difference (which is terrible since I just completed this question on the Fermat math contest for Waterloo earlier today, no problem, but I get thrown off in even easier math?)

 

[Biest]

read the question again. you don't even have to know the areas... it is simply asking for a ratio between the two

 

[mike_302]

well ya... Simple ratio is (10x^2)/27 : (22x^2)/9 ... sooo.. would I then put that into fraction form (not sure which on top vs bottom for this situation), then simplify as far as possible...?

 

[HallsofIvy]

"Determine how many times greater in size the penalty box is compared to the goal box."
You want "penalty box" over "goal box".

(22x^2) / 9 over (10x^2) / 27 which is the same as (22x^2)/9 times 27/(10x^2).