13.

Question

Find the perimeter of the polygon with vertices at (1, 3), (7, 3), (7, 7), and (4, 7).

13 units

18 units

22 units

20 units

Answer 1

To find the perimeter of the polygon with vertices at $(1,3)$, $(7,3)$, $(7,7)$, and $(4,7)$, we need to calculate the lengths of each of its sides and then add them together.

1. Calculate the distance between $(1,3)$ and $(7,3)$:
$$\text{Distance}=\sqrt{(7-1{)}^2+(3-3{)}^2}=\sqrt{6^2+0^2}=6$$

2. Calculate the distance between $(7,3)$ and $(7,7)$:
$$\text{Distance}=\sqrt{(7-7{)}^2+(7-3{)}^2}=\sqrt{0^2+4^2}=4$$

3. Calculate the distance between $(7,7)$ and $(4,7)$:
$$\text{Distance}=\sqrt{(4-7{)}^2+(7-7{)}^2}=\sqrt{(-3{)}^2+0^2}=3$$

4. Calculate the distance between $(4,7)$ and $(1,3)$:
$$\text{Distance}=\sqrt{(1-4{)}^2+(3-7{)}^2}=\sqrt{(-3{)}^2+(-4{)}^2}=\sqrt{9+16}=5$$

Now sum all the side lengths:
$$6+4+3+5=18$$

Therefore, the perimeter of the polygon is $\boxed{{\displaystyle 18}}$ units.