Question

What is the perimeter of a triangle with vertices located at (1, 3), (2, 6), and (0, 4), rounded to the nearest hundredth?

a. 7.40 units
b. 8.49 units
c. 9.07 units
d. 7.07 units

Answer 1

7.40 units

.....

Answer 2

The perimeter of a triangle is the sum of the lengths of all sides.
Using the distance formula
`d=√((x_2-x_1)^2+(y_2-y_1)^2)` calculate the lengths of the sides and then add them up.


`A=(1,3) \\ B=(2,6) \\ C=(0,4) \\ \\ \overline{AB}=√((2-1)^2+(6-3)^2)=√(1^2+3^2)=√(1+9)=√(10) \\ \overline{AC}=√((0-1)^2+(4-3)^2)=√((-1)^2+1^2)=√(1+1)=√(2) \\ \overline{BC}=√((0-2)^2+(4-6)^2)=√((-2)^2+(-2)^2)=√(4+4)=√(4 * 2)= \\ =2√(2) \\ \\ P=\overline{AB}+\overline{AC}+\overline{BC}=√(10)+√(2)+2√(2)=√(10)+3√(2) \approx 7.40`

The answer is A.