The 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?
Did you plot the points?
I would expect you to recognize that the shape is a rectangle.
Just count the distances.
Is there a way to mathematicaly solve it without plotting it?
well,
PQ = RS = 3
QR = SP = 4
so the perimeter is 2(3+4) = 14
To find the perimeter of the sandbox, we need to calculate the sum of the lengths of all the sides.
Let's find the length of each side using the distance formula:
The distance formula to find the length of a line segment between two points (x₁, y₁) and (x₂, y₂) is given by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the length of each side:
Side PQ:
P(12, 14) and Q(12, 17)
distance_PQ = √((12 - 12)² + (17 - 14)²)
= √(0² + 3²)
= √(0 + 9)
= √9
= 3 feet
Side QR:
Q(12, 17) and R(16, 17)
distance_QR = √((16 - 12)² + (17 - 17)²)
= √(4² + 0²)
= √(16 + 0)
= √16
= 4 feet
Side RS:
R(16, 17) and S(16, 14)
distance_RS = √((16 - 16)² + (14 - 17)²)
= √(0² + (-3)²)
= √(0 + 9)
= √9
= 3 feet
Side SP:
S(16, 14) and P(12, 14)
distance_SP = √((12 - 16)² + (14 - 14)²)
= √((-4)² + 0²)
= √(16 + 0)
= √16
= 4 feet
Now, add up all the side lengths to find the perimeter:
Perimeter = PQ + QR + RS + SP
= 3 + 4 + 3 + 4
= 14 feet
Therefore, the perimeter of the sandbox is 14 feet.