Can someone check over my work please?
The area of a rectangular piece of land is 280 square meters. If the length of the land was 5 meters less and the width was 1 meter more, the shape of the land would be a square.
Part A: Write an equation to find the width (x) of the land. Show the steps of your work. (5 points)
Part B: What is the width of the land in meters? Show the steps of your work. (5 points)

- anonymous

- jamiebookeater

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- anonymous

Here is my work:
Part A:
xy=A
xy=280
x+1=y-5
x= y-6
Part B:
(y-6)(y)=280
y^2-6y=280
y^2-6y-280=0
(y+14)(y-20)
The width of the land is 20 meters.

- IrishBoy123

have you thought about using "l" and "w" instead of "x" and "y" 'cos you may have got them the wrong way round.

- anonymous

so length would be: l-5
and width would be: w+1
so does that mean I would have to set l-5=w+1?

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## More answers

- anonymous

i dont think they're asking me to solve for x for part A, just to give them an equation...

- Mrhoola

I think I understand..

- Mrhoola

A rectangular area is usually denoted with 'L' for length and 'W' for width , since it is a rectangle L and W are not equal -Of course!
but the statement then says that if the rectangular area is to be a square under two conditions , That is:
i) L-5
ii) W +1
Right ? .
So if we think about the square part , all sides are the same . since that is true we can use another variable , lets call it 'X'
and we know the area of a square is x*x = Area

- anonymous

so that would be my answer to part A? x= 280/(x+5)?

- Mrhoola

Do you understand what I did ??

- anonymous

sort of?

- Mrhoola

x*x = area of a square
however we were given a rectangle but they told us that if one side is L -5 and the other side W+1 would make that rectangular into a sqaure
so I said , why not use the the area of the square equation
X = L-5
and
X = W +1 <--- This should totally make sense , right ?

- anonymous

yes i think so??

- Mrhoola

area of a rectangle is
L*W = area
let L = X+5
so
(x+5)*W = area
finally
W = area/(x+5)

- anonymous

okay i understand that!

- anonymous

is there something else i need to do for part a then?

- anonymous

or is that it

- IrishBoy123

@matenrouyes
i am sorry if i have added to any confusion
i was merely suggesting that you may have forgotten what x and y stand for
when you started out, did x stand for length or width. i'd say the latter.
so when you conclude rightly that y = 20 are you not concluding that length = 20 ?!
that was the only point i was making
and that was why i also suggested using more descriptive variable names

- IrishBoy123

so i paste your entire post into a text editor, i switch w for x and l for y and i get this:
Part A:
wl=A
wl=280
w+1=l-5
w= l-6
Part B:
(l-6)(l)=280
l^2-6l=280
l^2-6l-280=0
(l+14)(l-20)
see my point?

- anonymous

OHHH I SEE!!

- IrishBoy123

cool
apart from that, it's excellent

- anonymous

Thank you!! do you mind staying while i work it out to check it again?

- anonymous

OK:
so i think that for part a i had to find the equation of L, so this is what i did
Part A:
L-5=w+1
L= w+6
and then for part b, i would plug in what i got for A to get the width
(w+6)(w)=280
and when i solve it i get -20, and 14, and obviously you cant have negative meters so the width is 14?? @IrishBoy123

- Mrhoola

oops sorry for the wrong answer . (u_u)

- IrishBoy123

yes
adding in a few of the details that an instructor might wish to see and that you already included above:
\((w+6)w=280\)
\(w^2 + 6w -280 = 0\)
\((w+20)(w-14) = 0\)
\(w = 14\) or \(w = -20\)
so \(w = 14\)

- anonymous

but can you agree that what i put for part A is correct?

- IrishBoy123

ok
i'd stick with what you did originally a part from the fact you forgot what x and y were representing
so i pasted your work into a proessors and switched for w ad l and i got this:
Part A:
wl=A
wl=280
w+1=l-5
w= l-6
that is what you originally wrote and i think it's great because it:
1) connects W and L in terms of the 280 area; and
2) connects W and L in terms of how they might be equal/ form a square

- IrishBoy123

IOW, go with your original answer, just don't mix up width and length

- anonymous

alright, thank you both so much! now can you tell me how to give you metals? lol

- IrishBoy123

go up to a post by @Mrhoola and click Best Response

- anonymous

okie dokie!! Thank you both <3

- IrishBoy123

cool!!

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