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.
