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

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

Answer 2

The perimeter of the sandbox is 14 feet

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.