diebeatsthegmat wrote:
excuse me, i dont understand
if |x|+ |y|=10
so x=5, y=5,
x=-5 and y=5
x=5 y=-5
x=-5 y=-5
it could be. so we will have a square with 10 is the side
thus 10*10 =100
i dont understand why it could be 200. i dont understand why the side of the squre here turned into 200.?
As an alternative to Ajith's excellent explantion:
The thing you are missing is that the sides of the square aren't parallel to the x and y axis. They are parallel to y =x and y = -x
Forget the values of 5, they are just arbitrary points on each side of the square. We want the vertexes. See my modification to Ajith's picture, attached.
abs(x) + abs(y) =10 will create four lines (which ultimately enclose a square, see Ajith's earlier attachment)
x+y =10 -------- y = -x +10
x+y =-10 ------- y = -x - 10
x-y = 10 -------- y = x -10
x-y = -10 ------- y = x +10
Instead of using his formula, you can picture the vertexes of the square at the x intercepts of 10,-10 and the y intercepts of 10, -10
Now each side is the hypotenuse of a 45-45-90 right triangle. Hence, the sides are in the ratio x : x : x sqrt(2)
Each side of the triangle is 10, so the hypotenuse is 10sqrt(2).
Remember, the hypotenuse of the triangle is a side of the square.
Area of a square is side^2 = (10sqrt(2))^2 =200.
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