Question

The area of a rectangular piece of land is 260 square meters. If the length of the land was 5 meters less and the width was 2 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.

Answer 1

@SolomonZelman

Answer 2

Area = w × l

Answer 3

w × l = 260

l + 5 = w + 2

Answer 4

do you get the first equation i posted ?

Answer 5

yes

Answer 6

ok, and the second equation is the second sentence.
What the sentence is saying is that if:
1) length was 5 more (i.e. l+5)
2) width was 2 more (i.e. w+2)
then the shape would have been a square.

You know that in a square length and with are equal.
And when length is l+5 and width is w+2, then it is a
square. THEREFORE l+5=w+2

Answer 7

okay

Answer 8

so to find w or y the equation would be y=x+2+5 or y=x+7

Answer 9

the y ?

Answer 10

opps other way round.

Answer 11

w × l = 260
l + 5 = w + 2

all you need to do is to solve this system.

l + 5 = w + 2 → l=w-3

so substitute
w × (w-3) = 260
w² - 3w = 260

Answer 12

okay

Answer 13

solve for w (it will be a square root)

Answer 14

w is 13?

Answer 15

w²-3w-260=0


-(-3)±√[9-4(1)(260)]
----------------
2(1)

3±√[1049]
----------------
2

Answer 16

wait but shouldn't it be w + 2 = y - 5 ?

Answer 17

oh, tnx... my error

Answer 18

w × l = 260
l - 5 = w + 2

then,

w × l = 260
l = w + 7

Answer 19

w × (w + 7) = 260

Answer 20

13 is right

Answer 21

so the equation for w is w = l - 7 ?

Answer 22

well, -7 or +7, just depending on how you define l and w, and which way you sub.
but yes, there is an extra 7 between one dimension and the other dimension.

Answer 23

w × l = 260
l - 5 = w + 2

then,

w × l = 260
l = w + 7

then,

w × (w+7) = 260

then,

w² + 7w = 260

then,

w² + 7w - 260 = 0

(w + 20) (w - 13) = 0

Answer 24

so w=13

Answer 25

now, you nave to find l

Answer 26

20

Answer 27

l - 5 = w + 2
l - 5 = 13 + 2
l = 20


right !!

Answer 28

Thanks so much again!

Answer 29

yw