Question

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

Answer 1

Possible coordinates of square PQRS is

`P = (0,0)\\Q= (6,0)\\R= (6,6)\\S=(0,6)`

And many more sets of coordinates are possible.

Explanation:

Diagram of the given scenario is shown below,

Given that,

Perimeter of square is
`24 units`.

Area of square is
`32 sq. units`

So,

Perimeter of a square =
`4* side`

`4* side = 24 units\\`

`side = (24)/(4) = 6 units`

Now finding the coordinates of given square PQRS is

`PQ = 6units\\QR = 6 units\\RS = 6units\\SP= 6units`

Then using Distance formula we get,

For
`PQ` :
`\sqrt{(b-a)^(2) + 0^(2)} = 6units`

`b-a = 6units` .................(1)

`QR` :
`\sqrt{(b-b)^(2)+ (c-0)^(2) } = 6units`

`c=`±
`6` units

`RS` :
`\sqrt{(b-a)^(2) + (c-c)^(2)} = 6units`

`b-a = 6units`

`SP` :
`\sqrt{(a-a)^(2)+ (c-0)^(2) } = 6units`

`c=`±
`6` units

Solving equation (1) we found

`a=0, \ b= 6\\a=1,\ b=7\\a=2, \ b=8 \ etc.`

Hence Possible coordinates of square PQRS is

`P = (0,0)\\Q= (6,0)\\R= (6,6)\\S=(0,6)`

And many more sets of coordinates are possible.