Mathematics

The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and the width?


Answers

Quan336

4 years ago Comment

ok first list everything you know (what they told us) about this basketball court because this will come in handy. 

perimeter (p)=114 (they told us that this is the perimeter)
p=2w+2L  (using what we know about perimeters we can infer that this is the formula for a perimeter. this is just another way of writing p= w+L+w+L)
L=6+2w ("L" is length. they say that the length is 6 MORE, hence the plus sign, than 2 TIMES the width)

now lets put all this together. we want to find the length and width. we already have an idea of what the length is so we can plug that into our "p" formula...

p= 2w+ 2(6+2w).. now do a little simplifying 
p= 6w+12 

we know what "p" is so we can also plug that in
114= 6w+12 ..now get the variable on one side and the numbers on the other 
114-12=6w
[latex] \frac{102}{6}=w [/latex]
17=w

Great we just found what the width is BUT we aren't finished. we have to find the length. for this you just plug "w" back into your "p" formula. 

p= 2(17)+2L
remember that p=114
114= 34+2L
get "L" to one side
114-34=2L
[latex] \frac{80}{2}=L [/latex]
40=L

make sure you check your answers. simply plug "w" and "L" into your "p" formula if it equals 114 you did it right !!

Bhartman

4 years ago Comment

let width be x then
L = 6 + 2x (as per the question)
therefore perimeter = 2(L+B)
P=2(6+2x+x)
P=2(6+3x)
P=12+6x
acc. to question P=114 m
144 = 12 + 6x
6x=114-12
6x=102
x=[latex] \frac{102}{6} [/latex]
x=17
therefore width = 17 meters
then , length = 6 + 2x
where x=17 m
L=6+2(17)
L=6+34
L=40
therefore length and breadth of the basketball court is 17 m and 40 m respectively...