Liam is putting up fence around a garden. He has poles located at A(7, 7)
, B(16, 7)
, C(2, 2)
, and D(16, 2)
. Each unit on his coordinate grid represents 1 foot. How many feet of fencing does he need to fence in the garden? Round to the nearest foot.
To fence the garden, Liam needs to find the perimeter of the shape formed by the four poles.
To calculate the distance between two points on a coordinate grid, we can use the distance formula, which is given by:
√((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between each pair of adjacent poles:
- Distance between poles A(7, 7) and B(16, 7):
√((16 - 7)^2 + (7 - 7)^2) = √(9^2 + 0^2) = √(81) = 9 feet
- Distance between poles B(16, 7) and D(16, 2):
√((16 - 16)^2 + (7 - 2)^2) = √(0^2 + 5^2) = √(25) = 5 feet
- Distance between poles D(16, 2) and C(2, 2):
√((2 - 16)^2 + (2 - 2)^2) = √((-14)^2 + 0^2) = √(196) = 14 feet
- Distance between poles C(2, 2) and A(7, 7):
√((7 - 2)^2 + (7 - 2)^2) = √(5^2 + 5^2) = √(50) = 7.07 (rounded to the nearest foot) = 7 feet
Now let's add up these distances to find the total perimeter:
9 + 5 + 14 + 7 = 35 feet
Therefore, Liam needs about 35 feet of fencing to fence in the garden.
To find the perimeter of the garden, we need to add up the lengths of all four sides.
First, let's find the length of AB:
Distance between A(7, 7) and B(16, 7) using the formula: distance = √((x2 - x1)^2 + (y2 - y1)^2)
distanceAB = √((16 - 7)^2 + (7 - 7)^2)
distanceAB = √(9^2 + 0^2)
distanceAB = √(81 + 0)
distanceAB = √81
distanceAB = 9 feet
Next, let's find the length of BC:
Distance between B(16, 7) and C(2, 2) using the formula: distance = √((x2 - x1)^2 + (y2 - y1)^2)
distanceBC = √((2 - 16)^2 + (2 - 7)^2)
distanceBC = √((-14)^2 + (-5)^2)
distanceBC = √(196 + 25)
distanceBC = √221
distanceBC ≈ 14.87 feet
Now, let's find the length of CD:
Distance between C(2, 2) and D(16, 2) using the formula: distance = √((x2 - x1)^2 + (y2 - y1)^2)
distanceCD = √((16 - 2)^2 + (2 - 2)^2)
distanceCD = √(14^2 + 0^2)
distanceCD = √(196 + 0)
distanceCD = √196
distanceCD = 14 feet
Lastly, let's find the length of DA:
Distance between D(16, 2) and A(7, 7) using the formula: distance = √((x2 - x1)^2 + (y2 - y1)^2)
distanceDA = √((7 - 16)^2 + (7 - 2)^2)
distanceDA = √((-9)^2 + (5)^2)
distanceDA = √(81 + 25)
distanceDA = √106
distanceDA ≈ 10.30 feet
Now, let's find the perimeter by adding up the lengths of all four sides:
perimeter = distanceAB + distanceBC + distanceCD + distanceDA
perimeter ≈ 9 + 14.87 + 14 + 10.30
perimeter ≈ 48.17 feet
Therefore, Liam needs approximately 48 feet of fencing to fence in the garden.
To find out how many feet of fencing Liam needs to fence in the garden, we need to calculate the perimeter of the garden.
The garden is enclosed by four sides, and each side can be represented by a line segment connecting two points. The length of each side can be found using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances for each side:
Side AB:
Length_AB = sqrt((16 - 7)^2 + (7 - 7)^2)
= sqrt(9^2 + 0^2)
= sqrt(81 + 0)
= sqrt(81)
= 9 feet
Side BC:
Length_BC = sqrt((2 - 16)^2 + (2 - 7)^2)
= sqrt((-14)^2 + (-5)^2)
= sqrt(196 + 25)
= sqrt(221)
≈ 14.87 feet
Side CD:
Length_CD = sqrt((16 - 2)^2 + (2 - 2)^2)
= sqrt(14^2 + 0^2)
= sqrt(196 + 0)
= sqrt(196)
= 14 feet
Side DA:
Length_DA = sqrt((7 - 2)^2 + (7 - 2)^2)
= sqrt(5^2 + 5^2)
= sqrt(25 + 25)
= sqrt(50)
≈ 7.07 feet
Now, we can find the total perimeter by adding the lengths of all four sides:
Perimeter = Length_AB + Length_BC + Length_CD + Length_DA
= 9 + 14.87 + 14 + 7.07
≈ 44.94
Therefore, Liam needs approximately 44.94 feet of fencing to fence in the garden. Rounded to the nearest foot, he needs 45 feet of fencing.