Find the perimeter of the polygon with vertices of A(0, 0), B(4, 0) and C(2, 3). Round to the nearest tenth. Just enter one number as your answer
Can you please help me
A - B = 4
A - C = sqrt(4+9)
B - C = sqrt (4+9)
4 + 2 sqrt (13)
but my homework just wants one number as an answer not the square roots
use the distance formula to get the lengths of the sides:
4,√(2^2+3^2),√(2^2+3^2)
so the perimeter is 4+2√13
so use your calculator to evaluate 4+2√13
geez...
would the answer be 11.21
It says to nearest tenth, not hundredth
11.2
Of course! To find the perimeter of a polygon, we need to add up the lengths of all its sides. In this case, we have a triangle with vertices A(0, 0), B(4, 0), and C(2, 3).
To find the length of a side, we use the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates of the two points.
Let's calculate the length of each side:
- Side AB:
x-coordinate difference: 4 - 0 = 4
y-coordinate difference: 0 - 0 = 0
Length = √(4² + 0²) = √16 = 4
- Side BC:
x-coordinate difference: 2 - 4 = -2
y-coordinate difference: 3 - 0 = 3
Length = √((-2)² + 3²) = √13 = 3.6 (rounded to the nearest tenth)
- Side CA:
x-coordinate difference: 0 - 2 = -2
y-coordinate difference: 0 - 3 = -3
Length = √((-2)² + (-3)²) = √13 = 3.6 (rounded to the nearest tenth)
Finally, we add up the lengths of all sides to find the perimeter:
Perimeter = AB + BC + CA = 4 + 3.6 + 3.6 = 11.2
Therefore, the perimeter of the given polygon is approximately 11.2 units (rounded to the nearest tenth).