Ms. Wilson wishes to put a fence around a space in her yard to create a dog pen for Sonny and Hank. The space that she wants to fence in is shown below, where each unit on the graph represents one foot. The dimensions are,
A (-1,4) D (3,4)
B (-1,0) C (6,0)
How many feet of fencing will Ms. Wilson need to build the dog pen?
Can you explain in detail?
To calculate the perimeter of the dog pen, we need to add up the lengths of all the sides.
Given the coordinates of the four corners of the space Ms. Wilson wants to fence in, we can calculate the lengths of each side using the distance formula:
AB = √ ((x2 - x1)² + (y2 - y1)²)
BC = √ ((x2 - x1)² + (y2 - y1)²)
CD = √ ((x2 - x1)² + (y2 - y1)²)
DA = √ ((x2 - x1)² + (y2 - y1)²)
Using the coordinates given:
AB = √((-1 - (-1))² + (0 - 4)²) = √(0² + 4²) = √(0 + 16) = √16 = 4
BC = √(6 - (-1))² + (0 - 0)²) = √(7² + 0²) = √(49 + 0) = √49 = 7
CD = √(3 - 6)² + (4 - 0)²) = √((-3)² + 4²) = √(9 + 16) = √25 = 5
DA = √((-1 - 3)² + (4 - 4)²) = √((-4)² + 0²) = √(16 + 0) = √16 = 4
Adding up the four sides gives us:
Perimeter = AB + BC + CD + DA = 4 + 7 + 5 + 4 = 20 feet
Ms. Wilson will need 20 feet of fencing to build the dog pen.