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

Answer:

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.

Step-by-step 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 = $4\times side$

                                        $4\times side = 24 units$

                                              $side = \frac{24}{4} = 6 units$

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.