Football fields measure 100 x 53 1/3 yards excluding the two end zones, which each measure 10 x 53 1/3 yards. When comparing the football field with a basketball court that measures 94 x 50 feet, should one include or exclude the end zones in order for the two shapes to be the most similar?
please helpp me...
thank yu x )
jlwgreenwich
Favorite Answer
MimzKesler has missed the point completely - the question is about similarity not area. Ignore his brain work.
For two objects to be similar, you need the ratios of the corresponding sides to be in the same ratio. You want to find when will the Football field be MOST similar to the Basketball court. It is very unlikely that the corresponding ratios will be exact, but we need them to be as close as possible.
So let's compare corresponding measurements: First we will change the dimensions of the Basketball court to yards, by dividing the feet measurements by 3 to get 31⅓ by 16⅔
If we now compare the LENGTHs of each we get:
Football : Basketball = 100 : 31⅓ which is approximately 3.19 : 1 (without End Zone)
Football : Basketball = 110 : 31⅓ which is approximately 3.51 : 1 (including the End Zone)
If we now compare the WIDTHs of each we get:
Football : Basketball = 53⅓ : 16⅔ = 3.2 : 1
So you can see that there is a better correspondence by EXCLUDING the End Zone,
since the corresponding ratios are 3.19 : 1 for length and 3.2 : 1 for width - pretty close.
I hope this has helped.
Merryam&JC.
Well...
For the football field--> 100x53=5300, and 53x10=530, and 5300+530=5830,
For the basketball court --> 94x5=470 plus an extra 0=4700
So while comparing the two, 5830 is much too big to be similar, so i think that you shouldn't count the end zones for the two shaped to be similar. See? 5300...4700...only 6000 of difference.