Question Help: Video Question 3 Find the perimeter of a parallelogram with corner points at $$ (4,2),(5,6),(7,6) $$, and $$ (6,2) $$ Perimeter $$ =\square 0 / 7 \mathrm{pts} 3 \leftrightarrows 99 $$ Details Submit Question

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UpStudy AI · Accepted Answer

1. Label the given vertices as:
   - $$ A(4,2) $$
   - $$ B(5,6) $$
   - $$ C(7,6) $$
   - $$ D(6,2) $$

2. Compute the length of side $$ AB $$:
   $$
   AB = \sqrt{(5-4)^2 + (6-2)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17}
   $$

3. Compute the length of side $$ BC $$:
   $$
   BC = \sqrt{(7-5)^2 + (6-6)^2} = \sqrt{2^2 + 0^2} = \sqrt{4} = 2
   $$

4. Compute the length of side $$ CD $$:
   $$
   CD = \sqrt{(6-7)^2 + (2-6)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17}
   $$

5. Compute the length of side $$ DA $$:
   $$
   DA = \sqrt{(4-6)^2 + (2-2)^2} = \sqrt{(-2)^2 + 0^2} = \sqrt{4} = 2
   $$

6. Since opposite sides of a parallelogram are equal, the perimeter $$ P $$ is:
   $$
   P = 2(AB + BC) = 2(\sqrt{17} + 2) = 2\sqrt{17} + 4
   $$

Thus, the perimeter of the parallelogram is $$ 2\sqrt{17} + 4 $$.
The perimeter of the parallelogram is $$ 2\sqrt{17} + 4 $$.

Question Help: Video Question 3 Find the perimeter of a parallelogram with corner points at \( (4,2),(5,6),(7,6) \), and \( (6,2) \) Perimeter \( =\square 0 / 7 \mathrm{pts} 3 \leftrightarrows 99 \) Details Submit Question

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