a square has a perimeter of 24 units an area of 32 units and sides that are either horizontal or vertical the vertices are all located in the same quadrant where the x is positive what are the possible coordinates of the square

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sihanmintu sihanmintu · Answer 1 · 2020-04-04T10:34:58+02:00

Answer:

Possible coordinates of square PQRS is

[tex]P = (0,0)\\Q= (6,0)\\R= (6,6)\\S=(0,6)[/tex]

And many more sets of coordinates are possible.

Step-by-step explanation:

Diagram of the given scenario is shown below,

Given that,

Perimeter of square is [tex]24 units[/tex].

Area of square is [tex]32 sq. units[/tex]

So,

Perimeter of a square = [tex]4\times side[/tex]

[tex]4\times side = 24 units\\[/tex]

[tex]side = \frac{24}{4} = 6 units[/tex]

Now finding the coordinates of given square PQRS is

[tex]PQ = 6units\\QR = 6 units\\RS = 6units\\SP= 6units[/tex]

Then using Distance formula we get,

For [tex]PQ[/tex] : [tex]\sqrt{(b-a)^{2} + 0^{2}} = 6units[/tex]

[tex]b-a = 6units[/tex] .................(1)

[tex]QR[/tex] : [tex]\sqrt{(b-b)^{2}+ (c-0)^{2} } = 6units[/tex]

[tex]c=[/tex]±[tex]6[/tex] units

[tex]RS[/tex] : [tex]\sqrt{(b-a)^{2} + (c-c)^{2}} = 6units[/tex]

[tex]b-a = 6units[/tex]

[tex]SP[/tex] : [tex]\sqrt{(a-a)^{2}+ (c-0)^{2} } = 6units[/tex]

[tex]c=[/tex]±[tex]6[/tex] units

Solving equation (1) we found

[tex]a=0, \ b= 6\\a=1,\ b=7\\a=2, \ b=8 \ etc.[/tex]

Hence Possible coordinates of square PQRS is

[tex]P = (0,0)\\Q= (6,0)\\R= (6,6)\\S=(0,6)[/tex]

And many more sets of coordinates are possible.