Question

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)

Answer 1

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.

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

I think I understand..

Answer 6

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

Answer 7

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

Answer 8

Do you understand what I did ??

Answer 9

sort of?

Answer 10

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 ?

Answer 11

yes i think so??

Answer 12

area of a rectangle is

L*W = area

let L = X+5

so

(x+5)*W = area

finally
W = area/(x+5)

Answer 13

okay i understand that!

Answer 14

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

Answer 15

or is that it

Answer 16

@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

Answer 17

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?

Answer 18

OHHH I SEE!!

Answer 19

cool

apart from that, it's excellent

Answer 20

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

Answer 21

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

Answer 22

oops sorry for the wrong answer . (u_u)

Answer 23

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 \(w = 14\)

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

okie dokie!! Thank you both <3

Answer 30

cool!!