Question

Th vertices of a sandbox are p(12, 14), Q(12, 17), R (16, 17) and S (16, 14).the coordinates are measured in feet . What is the perimeter of the sandbox ?

Answer 1

Answer:

The perimeter of the sandbox is 14 feet

Step-by-step explanation:

To find the perimeter of the sandbox, we will find the distance between the points using the distance formula and then add them together

p(12, 14), Q(12, 17), R (16, 17) and S (16, 14)

Distance formula;

D = √ ($x_{2}$ - $x_{1}$)²  +  ($y_{2}$-$y_{1}$)²

p(12, 14)   Q(12, 17)

|PQ|  = √ ($x_{2}$ - $x_{1}$)²  +  ($y_{2}$-$y_{1}$)²

          = √(12-12)²  +  (17-14)²

           = √0² + (-3)²

            =√9

             =3

|PQ| = 3

Q(12, 17)      R (16, 17)

|QR| = √ ($x_{2}$ - $x_{1}$)²  +  ($y_{2}$ - $y_{1}$)²

         =√( 17 - 17)² + (16 - 12)²

         =√0² + 4²

          =√16

           = 4

|QR| = 4

R (16, 17)     S (16, 14)

|RS| = √ ($x_{2}$ - $x_{1}$)²  +  ($y_{2}$ - $y_{1}$)²

       =√(16-16)² + (14 -17)²

        =√0² + (-3)²

        =√9

        =3

|RS| = 3

S (16, 14)        p(12, 14)

|SP| =  √ ($x_{2}$ - $x_{1}$)²  +  ($y_{2}$ - $y_{1}$)²

        =√ (14 - 14)² + (12 - 16)²

         =√0² + (-4)²

          =√16

          =4

|SP| = 4

Perimeter = |PQ|  +  |QR| + |RS| + |SP|

                 = 3 + 4 + 3 + 4

                  =14

Since the coordinates are measured in feet, perimeter= 14 feet

Therefore the perimeter of the sandbox is 14 feet.

Answer 2

12,14 to 12,17 is a rise of 3 (14 to 17).
 12,14 to 16,14 is a move to the right of 4 (12 to 16)

That means the dimensions of the sandbox are 3ft  by 4ft and the perimeter is 2(l+w) or in this case 2 (3+4) or 14 ft