Answer:
Option 2 - 15.7 unit.
Step-by-step explanation:
Given : The image attached.
To find : The perimeter of the following shape?
Solution :
First we determine the coordinate of points,
A=(5,5)
B=(7,3)
C=(3,0)
D=(1,2)
Now, We apply distance formula to find the length of the sides.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance between AB,
[tex]AB=\sqrt{(7-5)^2+(3-5)^2}[/tex]
[tex]AB=\sqrt{(-2)^2+(2)^2}[/tex]
[tex]AB=\sqrt{4+4}[/tex]
[tex]AB=\sqrt{8}[/tex]
The distance between BC,
[tex]BC=\sqrt{(3-7)^2+(0-3)^2}[/tex]
[tex]BC=\sqrt{(-4)^2+(-3)^2}[/tex]
[tex]BC=\sqrt{16+9}[/tex]
[tex]BC=\sqrt{25}[/tex]
[tex]BC=5[/tex]
The distance between CD,
[tex]CD=\sqrt{(1-3)^2+(2-0)^2}[/tex]
[tex]CD=\sqrt{(-2)^2+(2)^2}[/tex]
[tex]CD=\sqrt{4+4}[/tex]
[tex]CD=\sqrt{8}[/tex]
The distance between DA,
[tex]DA=\sqrt{(5-1)^2+(5-2)^2}[/tex]
[tex]DA=\sqrt{(4)^2+(3)^2}[/tex]
[tex]DA=\sqrt{16+9}[/tex]
[tex]DA=\sqrt{25}[/tex]
[tex]DA=5[/tex]
The perimeter of the given shape is
[tex]P=AB+BC+CD+DA[/tex]
[tex]P=\sqrt{8}+5+\sqrt{8}+5[/tex]
[tex]P=2\sqrt{8}+10[/tex]
[tex]P=4\sqrt{2}+10[/tex]
[tex]P=4(1.41)+10[/tex]
[tex]P=5.64+10[/tex]
[tex]P=15.64[/tex]
[tex]P\approx15.7[/tex]
Therefore, Option 2 is correct.
The perimeter of the given shape is 15.7 unit.
