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.
A= (1,4)
B=(-1,0)
C= (6,0)
D= (3,4)
How many feet of fencing will Ms. Wilson need to build the dog pen?
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To find the total length of fencing needed, we need to add up the lengths of the four sides of the dog pen.
1. Side AB:
Using the distance formula, we get:
AB = √((-1-1)^2 + (0-4)^2) = √(4 + 16) = √20
2. Side BC:
BC = √((6+1)^2 + (0-0)^2) = √(49 + 0) = √49 = 7
3. Side CD:
CD = √((3-6)^2 + (4-4)^2) = √(9 + 0) = √9 = 3
4. Side DA:
DA = √((3-1)^2 + (4-0)^2) = √(4 + 16) = √20
Adding all four sides together:
Total fencing needed = AB + BC + CD + DA
Total fencing needed = √20 + 7 + 3 + √20
Total fencing needed = 2√20 + 10
Therefore, Ms. Wilson will need (2√20 + 10) feet of fencing to build the dog pen.