Find the perimeter of the parallelogram with these vertices(1,4), (-6,4), (5,-5),(-2,-5)
Give an exact answer (not a decimal approximation).
Simplify your answer as much as possible.
perimeter = twice the distance between (1, 4) and (-6, 4) + twice the distance between (1, 4) and (5, -5)
perimeter = \(2\cdot\sqrt{(4-4)^2+(-6-1)^2}\ +\ 2\cdot\sqrt{(-5-4)^2+(5-1)^2}\)
perimeter = \(2\cdot\sqrt{49}\ +\ 2\cdot\sqrt{97}\)
perimeter = \(2\cdot7\ +\ 2\cdot\sqrt{97}\)
perimeter = \(14\ +\ 2\sqrt{97}\)
perimeter = twice the distance between (1, 4) and (-6, 4) + twice the distance between (1, 4) and (5, -5)
perimeter = \(2\cdot\sqrt{(4-4)^2+(-6-1)^2}\ +\ 2\cdot\sqrt{(-5-4)^2+(5-1)^2}\)
perimeter = \(2\cdot\sqrt{49}\ +\ 2\cdot\sqrt{97}\)
perimeter = \(2\cdot7\ +\ 2\cdot\sqrt{97}\)
perimeter = \(14\ +\ 2\sqrt{97}\)