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.

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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.

Mathematics
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Area = w × l
w × l = 260 l + 5 = w + 2

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do you get the first equation i posted ?
yes
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
okay
so to find w or y the equation would be y=x+2+5 or y=x+7
the y ?
opps other way round.
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
okay
solve for w (it will be a square root)
w is 13?
w²-3w-260=0 -(-3)±√[9-4(1)(260)] ---------------- 2(1) 3±√[1049] ---------------- 2
wait but shouldn't it be w + 2 = y - 5 ?
oh, tnx... my error
w × l = 260 l - 5 = w + 2 then, w × l = 260 l = w + 7
w × (w + 7) = 260
13 is right
so the equation for w is w = l - 7 ?
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.
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
so w=13
now, you nave to find l
20
l - 5 = w + 2 l - 5 = 13 + 2 l = 20 right !!
Thanks so much again!
yw

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