Question

The area of a rectangular piece of land is 240 square meters. If the length of the land was 5 meters less and the width was 3 meters 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.

Part B: What is the width of the land in meters? Show the steps of your work.

Answer 1

@satellite73

Answer 2

we call the width x, then say the length is y, we get the areas \(xy=240\)

Answer 3

If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square.
i guess that means what? \(x-5=y+3\) ?
check it

Answer 4

yeah looks reasonalbe
seem right to you?

Answer 5

It looks pretty right to me but what would be the answer and how do you solve?

Answer 6

we can solve \[x-5=y+3\] for say \(y\) by subtracting \(3\) from both sides, giveing \[x-8=y\]

Answer 7

then since the area is \(xy=240\) replace \(y\) by \(x-8\) and get the equation in one variable, namely \[x(x-8)=240\] solve that for \(x\)

Answer 8

The answer would be 124 then?

Answer 9

idk i didn't do it
you want me to check?

Answer 10

seems unlikely

Answer 11

yes can you check please?

Answer 12

ok no

Answer 13

it is clearly not right \[124(124-8)\neq 240\] without doing the math

Answer 14

\[x(x-8)=240\] is a quadratic equation
you gotta multiplicity out first \[x^2-8x=240\] is a start

Answer 15

so would I factor?

Answer 16

after you subtract \(240\) and write \[x^2-8x-240=0\] if you can factor, yes

Answer 17

i suck at factoring, if it was me, i would cheat

Answer 18

haha :D it's ok I know how to factor

Answer 19

ok let me know what you get

Answer 20

cant you also use the quadratic formula?

Answer 21

sure if you want
this one has been cooked up to factor

Answer 22

since \(240=12\times 20\) you can use \[(x-20)(x+12)=0\]

Answer 23

ok and what would I write for my answer?

Answer 24

since if \((x+12)(x-20)=0\) you have \(x=-12\) or \(x=20\)
and since the side cannot be negative, you know \(x=20\) is the solution

Answer 25

That makes complete sense, I understand! Thanks so much again!!!!

Answer 26

yw (again)

Answer 27

wait wouldn't the solution be 12 not 20 since the negative number is 20?

Answer 28

\[x-20=0\\
x=20\]

Answer 29

sorry im still a bit confused

Answer 30

we factored it as \[(x+12)(x-20)=0\] and need to solve for \(x\)

Answer 31

set each factor equal to zero and solve \[x+12=0\] subtract 12 get \[x=-12\]
or \[x-20=0\] add 20 get \[x=20\]

Answer 32

oh Wow I understand it now :D Thanks AGAIN

Answer 33

yw

Answer 34

wait sorry again but what if it was (x - 12)(x + 20) how do you know which one is negative and which one to put as positive?

Answer 35

it wasn't

Answer 36

it was \[x^2-8x-240=(x+12)(x-20)\]

Answer 37

but how do you know which one will be negative and which one will be positive?

Answer 38

ooh
because you start with \[x^2-8x-240\] right?

Answer 39

right

Answer 40

two numbers that multiply to give \(-240\) and add to \(-8\)
so \(+12-20=-8\) and \(12\times (-20)=-240\) works

Answer 41

in other words, if you multiply out \[(x+12)(x-20)\] you get \[x^2-8x-240\]

Answer 42

yes I remember that now I don't know why but I completely forgot about that Thanks AGAIN im pretty sure this is the last question I needed to ask!

Answer 43

hey, keep 'em coming

Answer 44

haha :D

Answer 45

Well I guess i'm going to close this question now but thanks once again!