Question

find the perimeter of the parallelogram with these vertices. (3,6),(-5,6),(6, - 1),(-2, - 1) give an exact answer (not a decimal approximation). simplify your answer as much as possible. scratch area (not part of a

Explanation:

Step1: Calculate the length of one pair of sides

For the points \((3,6)\) and \((-5,6)\), since the \(y\) - coordinates are the same, use the distance formula \(d=\vert x_2 - x_1\vert\).
\(d_1=\vert-5 - 3\vert=\vert-8\vert = 8\)

Step2: Calculate the length of the other pair of sides

For the points \((3,6)\) and \((6,-1)\), use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
\(d_2=\sqrt{(6 - 3)^2+(-1 - 6)^2}=\sqrt{3^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}\)

Step3: Use the formula for the perimeter of a parallelogram

The perimeter formula of a parallelogram is \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of adjacent sides.
Here \(a = 8\) and \(b=\sqrt{58}\), so \(P=2(8+\sqrt{58})=16 + 2\sqrt{58}\)

Answer:

\(16+2\sqrt{58}\)